Prime quadruplet calculator

[Nathaniel]

Since it's never been explicitly constructed (as far as I know), here's a prime quadruplet calculator. It's just Dean Hickerson's twin prime calculator with a period 720 gun tacked on the left side of it to delete consecutive pairs.

In particular, a LWSS escapes past the left edge of the pattern at about generation 120N+1360 if and only if N, N+2, N+6, and N+8 are all prime. (note that the quadruplet (5,7,11,13) is not detected, since it overlaps with (11,13,17,19)).

Code: Select all

#C Prime quadruplet calculator created by Nathaniel Johnston on July 28, 2009.
#C Based on Dean Hickerson's twin prime calculator.
x = 460, y = 294, rule = B3/S23
432b2o$430b2ob2o13b2o$430b4o13b4o$431b2o14b2ob2o$113b3o11b3o319b2o$
113bo2bo10bo2bo$113bo6b3o4bo16b3o11b3o$113bo5bo2bo4bo15bo2bo10bo2bo$
114bo4b2obo5bo17bo4b3o6bo285b2o$146bo4bo2bo5bo284bo2bo$145bo5bob2o4bo
285bo2b2o$444bo2b2o$119bo8bo315b4o$119bobo5b3o278bo7bo$127bob2o14bo8bo
254bo7b2o$120bo2bo4b3o13b3o5bobo249bo4bo6b2o30b2o$121b3o4b2o13b2obo
258b5o29b4o4b4o$122bo20b3o4bo2bo280bo3bo3bo4b2ob2o$144b2o4b3o282bo6bo
6b2o$151bo279bo3bo5bo$432b4o$111b3o313b3o$110bo2bo311b2ob2o26b2o$113bo
46b3o264b3o17b4o4b4o$113bo46bo2bo268b4o10bo3bo4b2ob2o$112bo47bo270bo3b
o14bo6b2o$126b3o3b3o25bo274bo13bo$125bo2bo3bo2bo25bo272bo18bo$128bo3bo
6b3o3b3o253bo49bo$116b3o9bo3bo5bo2bo3bo2bo253b2o47bo2b2o$118bo8bo5bo7b
o3bo255b2o47bo5bo$117bo12bo10bo3bo9b3o293bobo2b2o$130bo9bo5bo8bo295bo
3b2o$129bobo11bo12bo296b3o$121b3o19bo$96bo13bo12bo18bobo$95b3o11b3o10b
o27b3o303b2o$95bob2o4bo5bob2o37bo12bo13bo277b4o$96b3o3b3o5b3o38bo10b3o
11b3o245bo13b2o15b2ob2o$96b2o3b2o2bo4b2o49b2obo5bo4b2obo244bo13b4o16b
2o$101bo3bo24b3o28b3o5b3o3b3o245b3o11b2ob2o$101bob2o57b2o4bo2b2o3b2o
261b2o$101b2o38b3o24bo3bo$169b2obo213bo$95b3o73b2o214b2o42b2o$94bo2bo
288b2o41b2ob2o$97bo78b3o250b4o$97bo78bo2bo246bo3b2o$96bo79bo248b2o$
176bo249bo3b2o$122b3o52bo251b4o$122bo2bo303b2ob2o$122bo26b3o279b2o$
112bo9bo25bo2bo227bo$111b3o8bo28bo226bo$75b3o11b3o19bob2o8bo27bo9bo
216b3o36b4o$74bo2bo10bo2bo20b3o36bo8b3o253bo3bo$77bo4b3o6bo20b2o36bo8b
2obo239b2o16bo$77bo4bo2bo5bo67b3o209bo21b4o4b4o14bo$76bo4bo8bo69b2o21b
o13bo9b2o163b2o18bo3bo4b2ob2o$117bo5bo58b3o11b3o7b4o161b2o23bo6b2o$
116b3o3b3o57bob2o4bo5bob2o6b2ob2o184bo$82b2o31b2obo3bob2o4b2o18bo5bo
26b3o3b3o5b3o8b2o189bo$82bo7bo24b3o5b3o4bobo16b3o3b3o25b2o3b2o2bo4b2o
198bo$89b3o24b2o5b2o6b2o9b2o4b2obo3bob2o29bo3bo28bo175bo2b2o$88b2obo
49bobo4b3o5b3o29bob2o30bo173bo5bo$88b3o29bo20b2o6b2o5b2o30b2o28bo3bo
174bobo2b2o$89b2o28b3o97b4o174bo3b2o$118bo3bo30bo28b3o26bo2b3o117bo64b
3o$152b3o26bo2bo25b2o2bobo116bo$92bo5bo52bo3bo28bo26bo2b3o116b3o$91b3o
3b3o18b2ob2o61bo34b4o179b2o$73b3o15bob2ob2obo20bo62bo34bo3bo178b4o25b
2o$73bo2bo15b3ob3o52b2ob2o66bo133bo27b2o15b2ob2o15b4o4b4o$73bo18b2o3b
2o33bo20bo67bo135b2o24b4o16b2o15bo3bo4b2ob2o$73bo57b2o41b3o3b3o16bo29b
o126b2o25b2ob2o36bo6b2o$74bo20bo35bobo7bo31bo2bo3bo2bo14b3o29bo154b2o
36bo$94bobo10bo33b2o33bo3bo17b3o25bo3bo16bo$93bo3bo9b2o31bobo33bo3bo
19bo26b4o17bo$78b2o14bobo9bobo57bo8bo5bo16bobo43bo3bo128b2o49b2o$77bob
o14b3o68b2o11bo19bo46b4o126b2ob2o48bobo$79bo85bobo10bo192bo3b4o49bob2o
$177bobo16bo172b2obo3b2o51b2o$102b3o90b2o92bo79bo3bo55bo$102bo2bo89bob
o90bo80b2obo3b2o$102bo66b3o72b3o41b3o80bo3b4o$102bo65bo2bo74bo128b2ob
2o50b2o$103bo67bo72bobo130b2o50b4o$171bo60bo11b2o166b2o15b2ob2o$170bo
59bo2bo177b4o16b2o$230bo2bo129b4o44b2ob2o$231bo5b2o8bo114bo3bo46b2o$
236b4o8bo117bo$236b2ob2o3bo3bo116bo$93b2o143b2o5b4o156b2o$92bobo308b2o
b2o$87b3o4bo304bo3b4o$87bo2bo90bo215b2obo3b2o$87bo92b2o215bo3bo$87bo
92bobo10bo13bo189b2obo3b2o$87bo104b3o11b3o52bo29bo29bo29bo47bo3b4o$88b
o103bob2o4bo5bob2o51b3o27b3o27b3o27b3o49b2ob2o$193b3o3b3o5b3o54bo29bo
29bo29bo50b2o11b2o$193b2o3b2o2bo4b2o54b2o28b2o28b2o28b2o19bo39b4ob2o$
198b2ob2o172bo38b6o$198bo2b3o165bo5bo15b4o20b4o$199bob2o167b6o14bo3bo
29b2o$201bo192bo28b4o$192b3o2bo3bo191bo29b2ob2o$191bo2bo3bobo224b2o$
194bo4bo221bo$194bo71b2o28b2o28b2o28b2o28b2o31bobo$193bo72bobo27bobo
27bobo27bobo27bobo32bo$184b3o80b2o28b2o28b2o28b2o28b2o36b2o$183bo2bo
236b2ob2o$186bo3b3o230b4o$186bo3bo2bo15bo214b2o$186bo3bo17b3o194b2o8b
4o$186bo3bo16b2obo192b2ob2o6b6o$185bo5bo15b3o135b2o52bo3b4o7b4ob2o$
208b2o134b4o46b2o2bobo3b2o12b2o$187b3o154b2ob2o44bo2b2o3bo$187bobo76b
2o28b2o28b2o18b2o46b2o2bobo3b2o$187b3o76bobo27bobo27bobo10bobo57bo3b4o
$267b2o28b2o22b2o4b2o9bo2b2o24b2o34b2ob2o$321bo17bobo16b4o4b4o35b2o5b
2o5b4o$165b3o11b3o5b3o156b2o9bo3bo4b2ob2o9bo29b2ob2o3bo3bo$165bo2bo10b
o2bo5bo155b2ob2o12bo6b2o11bo28b4o8bo$165bo6b3o4bo164b4o12bo15bo4bo29b
2o8bo$165bo5bo2bo4bo140b3o14bo7b2o30b5o$166bo4b2obo5bo129b4o5b5o13b2o
16bo$309bo3bo5b3ob2o11bobo12bo3bo62b2o$313bo8b2o26bo3bo9bo52bo2bo$305b
o6bo38bo12b6o42b2o3bo2bo$172b2o6bo88bo29bo7b3o32bo9b2o9bob3o44bo3b2ob
2o$172bo6b3o86b2o28b2o5bo6bo29b2o13b2o9bo48b2o$179bob2o130bo27bobo13bo
37b3o$180b3o126bo3bo83bo$127b2o6b2o43b2o128b4o53b2o27bo$126b4o4b4o228b
4o49b4o$126b2ob2o3b2ob2o227b2ob2o33bo13bo3bo$128b2o6b2o7b2o47b3o120b4o
30b2o15b2o35bo16bo$143b2ob2o46bo2bo118bo3bo28b2ob2o47bo3bo15bo$143b4o
16b3o28bo125bo14b4o10b4o49b4o$144b2o16bo2bo28bo9b2o8bo104bo14bo3bo11b
2o$165bo28bo8b4o8bo51bo70bo$165bo29bo7b2ob2o3bo3bo52bo68bo$140b4o20bo
40b2o5b4o48bo3bo$136b2o2bo2b2o120b4o$137bo3bo2b2o114b3o25b2o39b2o3b2o$
141bo2bo113b2ob2o24b4o36bo6bobo$142b2o67bo31b2o15b3o24b2ob2o34bo2bo6bo
$166b2o44b2o30b2o19b4o20b2o34b2o7b3o$101b5o58b2ob2o44bo29bo20bo3bo5bo
51b2o$100bo4bo31bo26b4o13b3o29bo54bo6bo6b2o$105bo32bo6b2o18b2o7bo6bo2b
o27bo54bo3bo3bo4b2ob2o$104bo29bo3bo4b2ob2o24bobo6bo56b5o29b4o4b4o$128b
4o3b4o4b4o26b2o6bo55bo4bo38b2o45b2o5b4o$127bo3bo12b2o36bo31bo27bo83b2o
b2o3bo3bo$131bo83bo25bo33bo50b4o8bo$123b2o2bo2bo65bo14bo3bo11b2o45bo3b
3o46b2o8bo$123b3o71bo14b4o10b4o43bo3bob3o$123b2o2bo2bo62bo3bo28b2ob2o
43bo6b2o$131bo62b4o30b2o15b2o28b5obo$127bo3bo111b2ob2o29b4o$128b4o89bo
bo19b4o31bo$187b4o31b2o20b2o12b2o$186bo3bo31bo36b2o$190bo67bo23b2o$
182b2o2bo2bo51b3o20b2o14b2ob2o$182b3o31bobo20bo3b2o18b4o13b4o$182b2o2b
o2bo27b2o20bobo2b2o17b2ob2o13b2o$190bo8b2o16bo20bo5bo20b2o$186bo3bo5b
3ob2o37bo2b2o$187b4o5b5o38bo$197b3o22b2o17bo$221b4o12bo$221b2ob2o12bo
6b2o$214bo2bo5b2o9bo3bo4b2ob2o$205b2o2bo4bo3bo16b4o4b4o$190b2o12bo2bo
2bo2bo4b2o24b2o$189bobo13b2o2b3o2bo3bo$176b2o11b2o14b3o2bo3bo2bo5b2o$
175bobo31bo11b2ob2o$177bo43b4o$222b2o3$220b2o$175bo43b4o$173bobo31bo
11b2ob2o$174b2o11b2o14b3o2bo3bo2bo5b2o$187bobo13b2o2b3o2bo3bo$188b2o
12bo2bo2bo2bo4b2o24b2o$203b2o2bo4bo3bo16b4o4b4o$212bo2bo5b2o9bo3bo4b2o
b2o$219b2ob2o12bo6b2o$219b4o12bo$123bo71b3o22b2o17bo$123b2o60b4o5b5o
38bo$122bobo59bo3bo5b3ob2o37bo2b2o$188bo8b2o16bo20bo5bo$180b2o2bo2bo
27b2o20bobo2b2o$180b3o31bobo20bo3b2o$180b2o2bo2bo51b3o$188bo$184bo3bo
31bo$185b4o31b2o20b2o$125b2o92bobo19b4o$21b6o31b2o63b2ob2o113b2ob2o$
20bo5bo28b3ob2o58bo3b4o65b4o30b2o15b2o$26bo28b5o54b2o2bobo3b2o65bo3bo
28b2ob2o$25bo30b3o54bo2b2o3bo73bo14b4o10b4o$114b2o2bobo3b2o68bo14bo3bo
11b2o$119bo3b4o86bo$123b2ob2o84bo$125b2o5b2o5b4o28b2o$100bo29b2ob2o3bo
3bo27bobo$101bo28b4o8bo20b2o7bo37bo$96bo4bo29b2o8bo20b4o45bo83bo$97b5o
60b2ob2o44bo84bo$164b2o44b2o79bo4bo20b2o8bo$139bo69bo82b5o19b4o8bo$
140bo175b2ob2o3bo3bo$135bo4bo177b2o5b4o$72bo54bo6b2o3b2o$70b3o52b3o10b
o64b2o5b4o$69bo54bo76b2ob2o3bo3bo107bobo$69b2o53b2o75b4o8bo97b2o6b2o3b
o$202b2o8bo98bobo5b3obob2o$139b4o170b2o4b3o4bo$124bo13bo3bo169bo9bo3bo
$125bo16bo180b3o$121bo3bo15bo181bo$122b4o$327bo$317b2o9bo$314b3ob2o4bo
3bo$314b5o6b4o$285b2o4b2o22b3o$285bo3b2ob2o$64b2o223b4o16b2o$64bo225b
2o15b2ob2o$307b4o$155b2o151b2o$80bo73b4o$79bobo65bobo4b2ob2o$38b2o29b
2o7bob2o74b2o15b2o132bo$38bo2bo26bobo6b2ob2o10b2o54bo22b2ob2o94b3o34b
2o$54b2o11bo6b3obob2o11bo54bo22b4o94b5o32bob2o$56bob2o7bo2bo2bo2bo2bob
o66bo23b2o95b3ob2o31bobo$38bob2o10bo2bo2bo8bo6b2o4bo191b2o32b2o$33b2o
2bobo12bobo13bobo$17b2o14bo4bo14bo15b2o17b2o58bo22bo$18bo18bo51bo58bo
22b2o128bo$18bobo7b2o4bo2bo15b2o26bobo64bo21bob2o113b2o13bo6b2o$19b2o
7bo24bo28b2o86bobo113bobo9bo3bo4b2ob2o3b2o8bo$25b2o55bo64bobo20b2o116b
o10b4o4b4o3b4o8bo$24b3o281b2o4b2ob2o3bo3bo$25b2o20b3o266b2o5b4o$5bo10b
o11b2o16bo3bo36b3o75bo126b2o$3b3o10b3o9bo8bo63b2o63bo6b2o116bobo$2bo5b
o4bo5bo16b2o7bo5bo49bobo58bo3bo4b2ob2o117bo$bob6o4b6obo24b2o3b2o51bo
41b2o16b4o4b4o146b2o$bobo14bobo82b2o38b2ob2o24b2o146b2ob2o$2o4b3o4b3o
4b2o121b4o36b2o112b2o22bo2bo$2bo2bo2bo4bo2bo2bo77b2o45b2o36b4o110bobo
22bo2bo$2bob4o6b4obo77bobo82b2ob2o111bo23b2o$3b3o10b3o80bo84b2o$50b2o
30b2o15b2o76bobo$45bo4bo32b2o91bo2b2o121b2o21bo$15bo29bo5b3o28bo94bobo
121bobo22bo$3b2o10b2o10b2o16bo7bo130b2o117bo3bo14bo3bo$4bo11bo9bo2bo
10bo4bo136b2ob2o3b2o8bo105bo3bo12b4o$15bo11b2o11b2o4bo135b4o3b4o8bo
104bo2b2o$8b2o5b3o19b2o144b2o4b2ob2o3bo3bo109bo$8bo2bobo2b2o19b5o3bo
29bo80b5o30b2o5b4o105b2o$8bob3o3b2o17b2o2b3ob2o30b2o78bo4bo$12bobo19b
3o26bobo8bobo83bo$13bo15b2o4b2o26bo3bo91bo$29b3o21b2o12bo10b2o117bo$
21b2ob3o2b2o22bo14bo7bo2bo118b2o$20bo3b5o38bo7bo12bo110bo$27b2o34bo3bo
7bo11b2o110bo$19bo4b2o11b2o24bobo9bo122bo$20bo4bo10bo2bo36bo2bo$20bo
16b2o39b2o$20bo24b2o153bo$20bo24bo155bo$197bo3bo$181b4o13b4o$180bo3bo$
184bo$183bo!

[Nathaniel]

While I'm making things like this, here is a cousin prime calculator. It finds all of the cousin primes except for the first one: (3,7). A LWSS escapes past the left edge of the pattern at about generation 120N + 840 if and only if (N,N+4) are cousin primes. This one works by having two p720 guns pick off the appropriate prime numbers, using reactions similar to (but not the same) as the twin primes calculator.

Code: Select all

#C Cousin prime calculator created by Nathaniel Johnston on July 29, 2009.
#C Based on Dean Hickerson's prime number calculator.
x = 439, y = 296, rule = B3/S23
410b4o$409bo3bo12bo2bo$413bo16bo$93bo13bo301bo2bo13bo3bo$92b3o11b3o
318b4o$91b2obo5bo4b2obo15bo13bo$91b3o5b3o3b3o15b3o11b3o$92b2o4bo2b2o3b
2o15bob2o4bo5bob2o$98b3o23b3o3b3o5b3o284b2o$124b2o3b2o2bo4b2o284bo2b2o
$131b3o289b3o2bo$423bo4bo$99bo6b3o314b5o$99bo6bo2bo286bo27b2o$99bo6bo
16b3o6bo254b2o8bo$100bobo3bo15bo2bo6bo251b3ob2o5b3o21b2o5bo2bo$100bobo
4bobo15bo6bo251b5o29b4o8bo$100b3o22bo3bobo253b3o30b2ob2o3bo3bo$122bobo
4bobo281b2o5b2o5b4o$129b3o279b2ob2o$91bo315bo3b4o$90b3o312b2obo3b2o$
90bob2o46bo264bo3bo17b2o5bo2bo$91b3o45b3o263b2obo3b2o12b4o8bo$91b2o45b
2obo265bo3b4o11b2ob2o3bo3bo$106bo5bo25b3o270b2ob2o12b2o5b4o$105b3o3b3o
25b2o272b2o$105bob2ob2obo5bo5bo$96bo9b3ob3o5b3o3b3o254bo49bobo$96b2o8b
2o3b2o5bob2ob2obo255bo46b2o3bo$95bobo21b3ob3o9bo244b3o46b3obob2o$119b
2o3b2o8b2o293b3o4bo$108b3o23bobo295bo3bo$101bo7bo323b3o$101b2o18b3o
309bo$74b3o11b3o9bobo19bo7bo$74bo2bo10bo2bo37b2o303bo2bo$74bo6b3o4bo
40bobo9b3o11b3o280bo$74bo5bo2bo4bo51bo2bo10bo2bo258bo2bo14bo3bo$75bobo
2bo3bo4bobo18bo32bo4b3o6bo244bobo15bo14b4o$79b2obobo25bo32bo4bo2bo5bo
244b2o12bo3bo$79b2ob2o26bo10bo18bobo4bo3bo2bobo246bo13b4o$80b3o38bo25b
obob2o$75bo45bo26b2ob2o213bo$74b3o72b3o215bo41b4o$74bob2o78bo208b3o40b
o3bo$75b3o77b3o254bo$75b2o77b2obo246b2o2bo2bo$154b3o247b3o$102bo52b2o
247b2o2bo2bo$101b3o308bo$100b2obo25bo278bo3bo$100b3o25b3o278b4o$90b3o
7b3o25bob2o$55bo13bo20bo2bo7b2o26b3o225bobo37b2o$54b3o11b3o19bo38b3o7b
3o215b2o37b4o$54bob2o4bo5bob2o18bo38b2o7bo2bo216bo37b2ob2o$55b3o3b3o5b
3o19bobo47bo231b2o5bo2bo14b2o$55b2o3b2obo5b2o70bo209bo20b4o8bo$138bobo
20b3o11b3o7bo2bo163bo19b2ob2o3bo3bo$95b3o3b3o57bo2bo10bo2bo10bo160b3o
21b2o5b4o$94bo2bo3bo2bo56bo6b3o4bo9bo3bo$61b2o34bo3bo7b2o17b3o3b3o24bo
5bo2bo4bo10b4o$61b2o5b3o26bo3bo7bobo15bo2bo3bo2bo24bobo2bo3bo4bobo198b
obo$67bo2bo23bobo5bobo5b2o9b2o7bo3bo31b2obobo203b2o3bo$70bo49bobo7bo3b
o31b2ob2o29b2o173b3obob2o$70bo27b3o19b2o5bobo5bobo29b3o28b2ob2o172b3o
4bo$67bobo28b3o61bo31bo3b4o176bo3bo$98b3o30b3o27b3o25b2o2bobo3b2o178b
3o$131b3o27bob2o24b4o3bo115bobo64bo$70b3o3b3o52b3o28b3o24b2o2bobo3b2o
111b2o$53bo16bo2bobo2bo19b3o61b2o30bo3b4o111bo66bo2bo$52b3o15bo7bo19b
3o97b2ob2o181bo16b2o5bo2bo$51b2obo15bo7bo52b3o66b2o134bo25bo2bo14bo3bo
15b4o8bo$51b3o17bobobobo32b2o19b3o20bo5bo176bo28bo14b4o15b2ob2o3bo3bo$
52b2o56bobo40b3o3b3o15b3o155b3o24bo3bo35b2o5b4o$74bo35bo9b2o31bob2ob2o
bo46b2o153b4o$73b3o10b2o31bobo32b3ob3o16bo2bo25b2ob2o$72b2ob2o8bobo33b
o32b2o3b2o16bob2o25b4o16b2o$57b2o13b2ob2o10bo56b2o61b2o15b2ob2o126b4o
48b2o$58b2o13bobo68bobo31bo45b4o126bo3bo47b2ob2o$57bo16bo69bo11b3o66b
2o122b2o7bo48bo2bo$82bo74bo16b2o172b4o2bo2bo49bo2bo$81b3o90bobo170bo3b
2o55b2o$80b2obo65bo24bo49bo42bobo78b4o2bo2bo$80b3o65b3o73b2o41b2o80b2o
7bo$81b2o65bob2o71bob2o41bo85bo3bo49bo2bo$149b3o71bobo129b4o53bo$149b
2o72b2o165bo2bo14bo3bo$210b3o130b2o49bo14b4o$209b3o130b4o44bo3bo$215bo
2bo123b2ob2o44b4o$219bo6b2o116b2o$215bo3bo4b2ob2o$72b2o142b4o4b4o155b
4o$67bo5b2o150b2o155bo3bo$66b3o3bo304b2o7bo$65b2obo90b2o215b4o2bo2bo$
65b3o91bobo213bo3b2o$65b3o91bo11b3o11b3o188b4o2bo2bo$66b2o103bo2bo10bo
2bo51bo29bo29bo29bo46b2o7bo$171bo6b3o4bo54b3o27b3o27b3o27b3o49bo3bo$
171bo5bo2bo4bo57bo29bo29bo29bo49b4o7b6o$172bobo6bo4bobo53b2o28b2o28b2o
28b2o59bo5bo$176bo176b2o16b2o26bo$177bo4bo166b4ob2o14b4o19bo4bo$182bo
166b6o15b2ob2o20b2o5bo2bo$172bo7bo169b4o18b2o32bo$171b3o5b2o221bo3bo$
171bob2o2b3o223b4o$172b3o3bo220bo$172b2o71b2o28b2o28b2o28b2o28b2o33b2o
$164bo80bobo27bobo27bobo27bobo27bobo31bo$163b3o80b2o28b2o28b2o28b2o28b
2o35b4o$163bob2o3bo231bo3bo$164b3o2b3o234bo$164b3ob2obo15b3o205b2o5bo
2bo$164b3ob3o15bo2bo193b4o6bo4bo$164b2o3b2o18bo192bo3bo12bo$189bo133bo
2bo51bo7bo6bo5bo$167bo18bobo138bo45b7o2bo2bo8b6o$166bobo154bo3bo44bo2b
3ob2o$165bo3bo75b2o28b2o28b2o17b4o45b7o2bo2bo$166bobo76bobo27bobo27bob
o11b3o56bo7bo$167bo78b2o28b2o22b2o4b2o9b2ob2o16b2o5bo2bo33bo3bo12b2o$
145bo13bo7bo132b2o17b3o15b4o8bo33b4o3b4o4b4o$144b3o11b3o5b3o155b4o9b2o
b2o3bo3bo39bo3bo4b2ob2o$143b2obo5bo4b2obo5b3o154bo3bo11b2o5b4o9b2o32bo
6b2o$143b3o5b3o3b3o140bo26bo28b3ob2o27bo2bo$144b2o4bo2b2o3b2o130b2o6bo
3bo13b2o5bo2bo29b5o$150b3o136b4o10bo11bobo39b3o$289b2ob2o4bo4bo13bo15b
2o62b2o$291b2o6b5o25b2o12bob3o48bo2bo$287bo42b3o9bo4bo43b2o3bo2b2o$
151b2o5b3o86b2o28b2o6bobo33b2o8bo16bo42b2o2bo2b2o$151b2o5bo2bo85b2o28b
2o8bo32bobo13b2o7b2o28bo19b4o$158bo132b2o29bo13b2o37b2o$158bo130b2ob2o
80bobo$105bo2bo4bo2bo42bobo127b4o52bo2bo50b2o$109bo7bo172b2o57bo48b4o$
105bo3bo3bo3bo56bo122b2o46bo3bo48b2ob2o$106b4o4b4o5b4o46b3o120b4o29b4o
13b4o33b2o15b2o$122bo3bo16bo28b2obo120b2ob2o14b2o11bo3bo48b2ob2o$126bo
15b3o27b3o123b2o14b4o14bo48b4o$122bo2bo16bob2o26b3o7bo2bo128b2ob2o9bo
2bo50b2o$143b3o27b2o11bo6b2o121b2o$120b2o21b2o37bo3bo4b2ob2o50b2o$119b
5o59b4o4b4o49b2ob2o$115b2o2bo4bo67b2o46bo3b4o$116bo2b3o2bo113b2obo3b2o
19bo2bo43b2o$120bo2b2o113bo3bo27bo36b3o3bobo$121b2o68bo30b3o13b2obo3b
2o19bo3bo33b3o6bob2o$81b3o60b4o43b2o31bo15bo3b4o19b4o33bo9b2o$80b5o58b
o3bo13bo30b2o29bo20b2ob2o55b3o7bo$80b3ob2o61bo12b3o28b2o53b2o5b2o5b4o$
83b2o31b2o5b4o16bo2bo5bo6b2obo55b3o30b2ob2o3bo3bo$108b2o4b2ob2o3bo3bo
26b2o4b3o55b5o29b4o8bo51b2o$107b4o3b4o8bo25b2o6b2o55b3ob2o29b2o5bo2bo
43b4o4b4o$107b2ob2o3b2o5bo2bo94b2o83bo3bo4b2ob2o$109b2o82b2o63bo50bo6b
2o$102bobo86b2ob2o9bo2bo44bo3bo2bo44bo2bo$101bo2b2o69b2o14b4o14bo42b2o
7bo$102bobo68b2ob2o14b2o11bo3bo43b2o6bo$27b2o24b2o54b2o62b4o29b4o13b4o
27b2o4b2o$27bo17bo8bo52b2ob2o62b2o46bo3bo32bo$44b3o60b4o56b2o33bo23bo
29b2o$47bo60b2o56b4o30bobo19bo2bo11b3o$43bob2o119b2ob2o30b2o36bo$42bob
2o122b2o51bo16bo21b4o$161bobo57b3o18bo2bo13bo3bo$160bo2b2o32bo22bo3bo
21bo16bo$16bo144bobo31bobo19b3o4bo17bo3bo12bo2bo$12bo2bo21b3o2b3o123b
2o6b5o15b2o19b3obob2o18b4o$15bobo2bo145b2ob2o4bo4bo36b2o3bo$13bob3o3bo
144b4o10bo38bobo$13b2o4b3o145b2o6bo3bo20bo2bo$13bobo20b2obo137bo26bo$
14bo20b2obo161bo3bo11b2o5b4o$13b2obo8bo8bo166b4o9b2ob2o3bo3bo$14b2o9b
2o8b3o23bo122b2o6b2o2b3o15b4o8bo$36bo17bo4b3o107b2o12bo2b2o2bob2o2b3o
16b2o5bo2bo$53b2o3bo109bobo12bo3b2obob2o2b3o$58b2o95b2o11b2o14bob2o2bo
10b4o$11bo14bo129b2o27bo14bo3bo$10bob2o10b2obo127bo48bo$10bob2ob2o4b2o
b2obo172bo2bo$8b2o2b2ob2o4b2ob2o2b2o$9bobo14bobo$9bob6o4b6obo24b2obob
2o138bo2bo$10bo5bo4bo5bo25bo5bo93bo48bo$11b3o10b3o9b2o16bo3bo95b2o27bo
14bo3bo$13bo10bo10bobo17b3o95b2o11b2o14bob2o2bo10b4o$34b3o4b2o123bobo
12bo3b2obob2o2b3o$33b3o4bo2bo123b2o12bo2b2o2bob2o2b3o16b2o5bo2bo$34b3o
5bo139b2o6b2o2b3o15b4o8bo$27b2o6bobo23b2o136b4o9b2ob2o3bo3bo$26bobo7b
2o21bo2bo135bo3bo11b2o5b4o$26bo15b4o129bo26bo$25b2o14bo4bo55b2o61b2o6b
o3bo20bo2bo$41bo3bobo11b2obo38bobo60b4o10bo38bobo$42bo3bobo12bobo2b2o
35bo60b2ob2o4bo4bo36b2o3bo$48bo13bo4bo98b2o6b5o15b2o19b3obob2o$48bo14b
o95bobo31bobo19b3o4bo$45bo2bo14bo2bo91bo2b2o32bo22bo3bo$46b2o111bobo
57b3o$166b2o51bo$164b2ob2o30b2o$164b4o30bobo19bo2bo$b4o98b4o58b2o33bo
23bo$6o29b5o62bo3bo65b2o46bo3bo$4ob2o27bo4bo58bo7bo64b4o29b4o13b4o$4b
2o33bo53b7o2bo2bo65b2ob2o14b2o11bo3bo$34bo3bo53bo2b3ob2o72b2o14b4o14bo
$36bo56b7o2bo2bo83b2ob2o9bo2bo$98bo7bo84b2o$102bo3bo12b2o$103b4o3b4o4b
4o28b2o$109bo3bo4b2ob2o28b2o$79b2o32bo6b2o19bo2bo5bo$76b3ob2o27bo2bo
32bo43b2o$76b5o60bo3bo44b2o82b2o$77b3o62b4o43b2o80b3ob2o18bo2bo$189bo
81b5o23bo6b2o$118b2o152b3o20bo3bo4b2ob2o$113bo5b2o175b4o4b4o$104bo8b2o
3b2o70b2o113b2o$102b3o13bo62b4o4b4o$101bo78bo3bo4b2ob2o105bo$101b2o81b
o6b2o97b2o6bo3b3o$119b2o59bo2bo106bob2o3bo3bob3o$118b4o170b2o4bo6b2o$
118b2ob2o169bo6b5obo$103b2o15b2o179b4o$101b2ob2o196bo$101b4o$102b2o$
294b5o7b2o$293bo4bo5b2ob2o$298bo5b4o$264b2o3b4o20bo3bo7b2o$264b2o2bo3b
o22bo$272bo14b4o$268bo2bo14bo3bo$290bo$133bo2bo149bo2bo$137bo$133bo3bo
$101b2o24bo6b4o13b4o95bo35b2o$101bo48bo3bo93bo3bo32bo2bo$102b3o21b3o
25bo98bo31bo2bo$104bo45bo2bo94bo4bo30b2ob2o$249b5o31b2o2$75b2o73b2o$
64bo9bobo49b3o20bo2bo$63b2o11bo72bo2bo113b2o12b2o5b4o$80b4o43bo20b2ob
2o114b2o9b2ob2o3bo3bo2bo2bo$64bo14bo4bo64b2o115bo11b4o8bo6bo6b2o$63bob
o12bobo3bo194b2o5bo2bo3bo3bo4b2ob2o$58b2o2bo2bo11bobo3bo210b4o4b4o$42b
2o14b2obo15bo193b2o30b2o$43bo18b2o9bo3bo66b2o5b4o117b2o$43bobo5b2o19bo
bo2bo2bo61b2ob2o3bo3bo116bo$44b2o5bo2bo17bo5b2o43b4o15b4o8bo144b4o$55b
o17bo48bo3bo16b2o5bo2bo145bo2b2o$55bo70bo34bo2bo111b2o22bo2b2o$55bo66b
o2bo39bo111b2o21bo2bo$30bo10bo9bo2bo15b2o3b2o84bo3bo110bo24b2o$28b3o
10b3o7b2o17bobobobo85b4o$27bo5bo4bo5bo26b5o81b3o$26bob6o4b6obo26b3o80b
2ob2o121b2o$26bobo14bobo27bo83b3o122b2o20b2o$25b2o2bo2b2o4b2o2bo2b2o
115b4o115bo20b2ob2o$27b2o2bobo4bobo2b2o116bo3bo2bo2bo113b2ob2o12b4o$
27bobo12bobo120bo6bo6b2o107b3o12b2o$28bo14bo92b3o22bo2bo3bo3bo4b2ob2o
104b4o$75b2o58b5o29b4o4b4o$70bo4bo59b3ob2o37b2o$70b2o4b3o59b2o$29bo48b
o$28b2o147bo$37bo11b4o124b2o$36b5o8bob2o9b2o114b2o$35bo3b3o8b2o2bo7bo
114b2o$36b2o5bo11bo6bob2o$37b4o13bo9bobo$38b2o2bo10bo8bo$40b2o7bobo9bo
$50b2obo6bo118b2o$53bo7bo2b2o95b2o14b2ob2o$52b2o9b2obo93b4o13b4o$63b4o
93b2ob2o13b2o$162b2o2$44bo26bo$44b2o24b2o!

[calcyman]

Impressive! Presumably the Cousin Prime calculator could be trivially modified to find all pairs of prime numbers of the following form:

q = p + 2k

(q and p are prime numbers; k is a positive integer.)



Have you seen the Fermat Prime Calculator? It's eventual growth is related to an unsolved mathematical problem: The pattern exhibits growth if and only if no Fermat Primes exist above 65 537, or 2^(2^4)+1. All known Fermat Numbers above 65 537 are composite, but there is no proof that higher Fermat Primes do, or do not, exist.

[Nathaniel]

Impressive! Presumably the Cousin Prime calculator could be trivially modified to find all pairs of prime numbers of the following form:

q = p + 2k

(q and p are prime numbers; k is a positive integer.)

Surprisingly, doing this isn't as easy as you'd think and I haven't figured out a "compact" way to do it for k >= 3 yet (by compact I mean requiring only one copy of the prime gun itself). The cousin prime gun takes advantage of the fact that all cousin primes except for the first pair are of the form (6n+1, 6n+5), so in particular two cousin prime pairs will never overlap (except for the first pair, which isn't detected), which makes the elimination logic not too difficult. However, once you get to k >= 3, this is no longer true. For example, the pair (11, 17) overlaps with (13, 19), so I'm not sure how (using just one LWSS stream) to make it work.

[calcyman]

so I'm not sure how (using just one LWSS stream) to make it work.

1. Use a fanout device to split the LWSS stream into two streams.

2. Rephase one of the streams by the desired amount.

3. Find the logical conjunction (Boolean AND) of the two streams.

[Nathaniel]

1. Use a fanout device to split the LWSS stream into two streams.

This is where I was getting stuck, actually. Do you know of such a device?

[Nathaniel]

This is a Mersenne prime calculator. It finds all of the Mersenne primes except for the first one (3). A LWSS escapes past the honeycomb near the bottom-left of the pattern at about generation 120N - 370 if and only if N is a Mersenne prime. The caber tosser that picks off the non-Mersenne primes is by Dean Hickerson (and inspired by Jason Summers' Fermat prime calculator), modified via an inline inverter and a p120 gun to eliminate non-Mersenne primes rather than eliminating Mersenne primes themselves.

Code: Select all

#C Mersenne prime calculator created by Nathaniel Johnston on July 30, 2009.
#C Based on Jason Summers' Fermat prime calculator.
x = 893, y = 590, rule = B3/S23
246b3o11b3o$246bo2bo10bo2bo$246bo6b3o4bo16b3o11b3o$246bo5bo2bo4bo15bo
2bo10bo2bo$247bobo2b2obo5bobo15bo4b3o6bo$279bo4bo2bo5bo$276bobo5bob2o
2bobo2$252bo8bo$252bobo5b3o$260bob2o14bo8bo$253bo2bo4b3o13b3o5bobo$
254b3o4b2o13b2obo$255bo20b3o4bo2bo$277b2o4b3o$284bo2$244b3o$243bo2bo$
246bo46b3o$246bo46bo2bo$243bobo47bo$259b3o3b3o25bo$248bo9bo2bo3bo2bo
25bobo$248bo12bo3bo6b3o3b3o$249b3o9bo3bo5bo2bo3bo2bo9bo$251bo6bobo5bob
o5bo3bo12bo$274bo3bo9b3o$262b3o6bobo5bobo6bo$262b3o$254b3o4bobobo9b3o$
229bo13bo12bo18b3o$228b3o11b3o10bo18bobobo4b3o$228bob2o4bo5bob2o37bo
12bo13bo$229b3o3b3o5b3o38bo10b3o11b3o$229b2o3b2o2bo4b2o16b2o31b2obo5bo
4b2obo$234bo3bo22b2o31b3o5b3o3b3o$234bob2o23b3o13b2o16b2o4bo2b2o3b2o$
234b2o41b2o22bo3bo$262b5o9b3o23b2obo$228b3o73b2o$227bo2bo42b5o$230bo
78b3o$230bo32b2o44bo2bo$227bobo32bo2bo43bo$262bo12b2o32bo$238b2o15b3o
5b3o8bo2bo32bobo$238b2o15bo2bo18bo$255bo18b3o5b3o15b2o$236bo8bo9bo3bo
21bo2bo15b2o$235b3o6b3o8bo28bo$208b3o11b3o9b5o5bob2o8bobo21bo3bo9bo8bo
$207bo2bo10bo2bo13b2o5b3o36bo8b3o6b3o$210bo4b3o6bo9b5o6b2o34bobo8b2obo
5b5o$210bo4bo2bo5bo10b3o54b3o5b2o$207bobo4bo6bobo11b2o56b2o6b5o10bo13b
o$219bo30bo5bo45b3o10b3o11b3o$213bo4bo30b3o3b3o45b2o10bob2o4bo5bob2o$
213bo34b2obo3bob2o4b2o18bo5bo26b3o3b3o5b3o$215bo7bo24b3o5b3o4bobo16b3o
3b3o25b2o3b2o2bo4b2o$215b2o5b3o24b2o5b2o6b2o9b2o4b2obo3bob2o29bo3bo$
216b3o2b2obo49bobo4b3o5b3o29bob2o$217bo3b3o29bo20b2o6b2o5b2o30b2o$222b
2o20bo7b3o$245bo5bo3bo30bo28b3o$243b3o17b2o20b3o7bo18bo2bo$225bo5bo30b
o2bo18bo3bo5bo22bo$224b3o3b3o18b2ob2o7b2o10b2o17b3o20bo$206b3o15bob2ob
2obo20bo20bo2bo36bobo$206bo2bo15b3ob3o43b2o7b2ob2o$206bo18b2o3b2o54bo
38b2o$206bo44bo3bo51b3o3b3o9b2o$207bobo18bo21bobobobo49bo2bo3bo2bo15bo
$211bobo13bobo21b5o28bo3bo20bo3bo9bo7b3o$211bo2bo11bo3bo20b2ob2o27bobo
bobo19bo3bo8b3o5b2obo$211bo15bobo22bobo29b5o17bobo5bobo4b5o4b3o$213b2o
12b3o22b3o29b2ob2o36b2o4b2o$285bobo22b3o8b5o$249bo35b3o22b3o9b3o$235b
3o12bo58bobobo8b2o$216b2o8b2ob2o4bo2bo9b3o39bo$215bobo8b2ob2o4bo53bo
12b3o$217bo8b2ob2o4bo53b3o9bo2bo$228bo7bobo65bo3b2o3b2o9bo$304bo4b2ob
2o9b2o$221b2o4b3o71bobo5b2ob2o9bobo$220bobo88bo$222bo$263b2o54bo$253b
2o8bobo52b2o$226b2o25b2o9b2o9b2o41bobo$225bobo46bobo8b2o$220b3o4bo46b
2o9b2o$220bo2bo90bo$220bo32bo2bo56b2o$220bo3bo26bobo9b2o48bobo10bo13bo
$220bo28b2o4b3o4bo2bo17bo2bo38b3o11b3o$221bobo28b5o6b2o10b2o9bobo36bob
2o4bo5bob2o$248bo3b5o17bo2bo4b3o4b2o35b3o3b3o5b3o$252bo2bo19b2o6b5o38b
2o3b2o2bo4b2o$250b2ob2o28b5o3bo39b2ob2o$249bo4bo29bo2bo24b2o17bo2b3o$
250bo34b2ob2o22b2o18bob2o$285bo4bo43bo$289bo35b3o2bo3bo$241b2o81bo2bo
3bobo$240bobo84bo4bo$242bo84bo$299bo24bobo$298b2o17b3o$298bobo15bo2bo$
319bo3b3o$315bo3bo3bo2bo15bo$315bo3bo3bo11b2o4b3o$319bo3bo16b2obo$316b
obo5bobo13b3o$341b2o$252b2o66b3o13b2o$252b2o9b2o55b3o13b3o$263bobo20b
2o32b3o11bo2bo$256b2o6b2o9b2o9b2o47b2o$255bobo16bobo$257bo16b2o22b3o
11b3o5b3o$284bo13bo2bo10bo2bo4b3o$283b2o13bo6b3o4bo20bo$283bobo12bo5bo
2bo4bo19b2o$299bobo2b2obo5bobo3bo3bo8bobo$318bo5bo$318bo5bo$328bo$304b
o8bo13b2o$304bobo5b3o5bobo4bobo$312bob2o5bo$305bo2bo4b3o$306b3o4b2o8bo
$307bo14b2o$322bobo$327b3o$327bo2bo$296b3o28bo$295bo2bo28bo3bo$298bo
28bo$298bo29bobo$295bobo$313bo$261b2o9b3o25bo11b2o$253bo7bo2bo9bo25bo
11bobo$252bo3b2o7bo7bo5bo21b3o$252bo5bo6bo12b4o21bo$253b5o7bo11b2obobo
3b2o$261bo2bo11b3obo2bo2b2o26b3o$261b2o14b2obobo31bo2bo$278b4o24b3o5bo
$279bo28bo5bo$307bo7bobo6$287b3o$289bo$288bo5$280b2o$279bobo$281bo27b
2o$309bo$307bobo$307b2o3$261b2o9b3o27b3o$253bo7bo2bo9bo29bo$252bo3b2o
7bo7bo5bo23bo$252bo5bo6bo12b4o$253b5o7bo11b2obobo3b2o$261bo2bo11b3obo
2bo2b2o$261b2o14b2obobo$278b4o13b2o$279bo14bobo$296bo6$287b3o$289bo$
288bo5$280b2o$279bobo$281bo27b2o$309bo$307bobo$307b2o3$261b2o9b3o27b3o
$253bo7bo2bo9bo29bo$252bo3b2o7bo7bo5bo23bo$252bo5bo6bo12b4o$253b5o7bo
11b2obobo3b2o$261bo2bo11b3obo2bo2b2o$261b2o14b2obobo$278b4o13b2o$279bo
14bobo$296bo6$287b3o$289bo$288bo5$280b2o$279bobo$281bo27b2o$309bo$307b
obo$307b2o3$261b2o9b3o27b3o$253bo7bo2bo9bo29bo$252bo3b2o7bo7bo5bo23bo$
252bo5bo6bo12b4o$253b5o7bo11b2obobo3b2o$261bo2bo11b3obo2bo2b2o$261b2o
14b2obobo$278b4o13b2o$279bo14bobo$296bo6$287b3o$289bo$288bo5$280b2o$
279bobo$281bo27b2o$309bo$307bobo$307b2o3$261b2o9b3o27b3o$253bo7bo2bo9b
o29bo$252bo3b2o7bo7bo5bo23bo$252bo5bo6bo12b4o$253b5o7bo11b2obobo3b2o
47b2o$261bo2bo11b3obo2bo2b2o46b2o$261b2o14b2obobo53bo$278b4o13b2o$279b
o14bobo$296bo5$316bo$287b3o27b2o$289bo26b2o$288bo2$380b2o$379b2o$381bo
$280b2o$279bobo$281bo27b2o$309bo$307bobo$307b2o3$261b2o9b3o27b3o$253bo
7bo2bo9bo29bo560b2o$252bo3b2o7bo7bo5bo23bo559b2ob2o13b2o$252bo5bo6bo
12b4o581b4o13b4o$253b5o7bo11b2obobo3b2o137b2o437b2o14b2ob2o$261bo2bo
11b3obo2bo2b2o136b2o456b2o$261b2o14b2obobo143bo$278b4o13b2o$279bo14bob
o566bo4b2o$296bo557bo7b3o3b2o9b2o$855b2o4b2ob2o12bo2bo$854b2o4b3ob3o
11bo2b2o$860b3ob2o11bo2b2o$839bo22bobo12b4o$837bo3bo7bo$287b3o552bo7b
2o$289bo547bo4bo6b2o30b2o$288bo549b5o29b4o4b4o$864bo2bo3bo3bo4b2ob2o$
470b2o372bo23bo6bo6b2o$469b2o374b2o17bo3bo2bo2bo$471bo372b2o8b2o9b4o$
280b2o571b2o5b3o$279bobo567b3o6b2ob2o26b2o$281bo27b2o542b2o5b3o17b4o4b
4o$309bo544b2o9b4o10bo3bo4b2ob2o$307bobo554bo3bo14bo6b2o$307b2o559bo
10bo2bo$864bo2bo18bo$834bo49bo$261b2o9b3o27b3o530b2o35bo11bo2b2o$253bo
7bo2bo9bo29bo529b2o37bo9bo5bo$252bo3b2o7bo7bo5bo23bo568b3o9bobo2b2o$
252bo5bo6bo12b4o590b3o9bo3b2o$253b5o7bo11b2obobo3b2o227b2o351b5ob3o9b
3o$261bo2bo11b3obo2bo2b2o226b2o353b3o3b2o$261b2o14b2obobo233bo353bo$
278b4o13b2o592b2o$279bo14bobo591b4o$296bo560bo13b2o15b2ob2o$856bo13b4o
16b2o$856b3o11b2ob2o$872b2o2$819bo$287b3o530b2o42b2o$289bo529b2o32bo8b
2ob2o$288bo555bo6bobo4bo3b4o$850bo2bo5bo3b2o$560b2o283bo4bo6bo2bo$559b
2o279bo4bo4bo2bo5bo3b2o$561bo277bo3bo7bobo4bo3b4o$280b2o557bobo11bo8b
2ob2o$279bobo558bo23b2o$281bo27b2o501bo$309bo501bo$307bobo501b3o36b4o$
307b2o540bo3bo$835b2o16bo$361bo442bo21b4o4b4o11bo2bo$261b2o9b3o87b2o
276b2o163b2o18bo3bo4b2ob2o$253bo7bo2bo9bo86b2o276b4o161b2o23bo6b2o$
252bo3b2o7bo7bo5bo359b2ob2o181bo2bo$252bo5bo6bo12b4o350b3o6b2o189bo$
253b5o7bo11b2obobo3b2o317b2o25bobo195bo$261bo2bo11b3obo2bo2b2o316b2o
27b3o15bo2bo163bo11bo2b2o$261b2o14b2obobo323bo27bo20bo163bo9bo5bo$278b
4o350b3o4bo11bo3bo162b3o9bobo2b2o$279bo352b3o2bo2bo11b4o162b3o9bo3b2o$
636bo6b2o2b3o117bo46b5ob3o9b3o$636bo6b2o2b3o116bo48b3o3b2o$636bo6b2o2b
3o116b3o47bo$637bo2bo11b4o179b2o$639bo11bo3bo178b4o25b2o$635b2o18bo
133bo13bo13b2o15b2ob2o15b4o4b4o$634bo16bo2bo135b2o10bo13b4o16b2o15bo3b
o4b2ob2o$659bo2bo126b2o11b3o11b2ob2o36bo6b2o$663bo154b2o33bo2bo$659bo
3bo13bo2bo$650b2o8b4o17bo$649b2o26bo3bo109bo18b2o33b3o13b2o$651bo26b4o
108bobo15b2ob2o31b4o13bobo$792b2o2b3o5bo3b4o32bo3bo12bob2o$796b3o3b2ob
o3b2o34b3o14b2o$309b2o356b2o53bo50bo18b2obo6bo3bo38b3o3b2o9bo$309bo
352bo4b2o52bo50bo20bo2b3o3b2obo3b2o40b2o$307bobo351b3o13b3o41b3o48b3o
21b3o5bo3b4o$307b2o351bo18bo128b2ob2o50b2o$660b5o7b2o3bobo130b2o22bo
27b4o$669bo7b2o95bo58bo11b2o15b2ob2o$775b2o56b3o8b4o16b2o$774b2o20b4o
44b2ob2o$670b2o5bo2bo114bo3bo46b2o$669b4o8bo117bo19bo$669b2ob2o3bo3bo
113bo2bo19bo$671b2o5b4o136b3o17b2o$836b2ob2o$824b3o5bo3b4o$821bo2b3o3b
2obo3b2o$677bo50bo92bobo6bo3bo$676bo50bo93bo2b3o3b2obo3b2o$394bo29bo
29bo29bo29bo29bo29bo29bo29bo29bo11b3o15bo32b3o94b3o5bo3b4o$394b3o27b3o
27b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o139b2ob2o$397bo29bo29bo
29bo29bo29bo29bo29bo29bo29bo29bo106b2o32b2o11b2o$396b2o28b2o28b2o28b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o61bo42bo4bo39b4ob2o$760b2o46bo38b6o
$730b2o27b2o41bo5bo15b4o20b4o$131b2o596b2o72b6o14bo3bo29b2o$132bo598bo
42bo52bo28b4o$132bobo6bobo236b2o391bo49bo2bo29b2ob2o$133b2o5bo2bo235b
2o392b3o71b3ob2o5b2o$123bo15b2o10bo6bo222bo17bo29bo29bo29bo29bo29bo29b
o29bo29bo168bo5bo5bo5bo5bo5bo7b2o5bo$123b4o10b2o3bo8bo5bobo238b3o27b3o
27b3o27b3o27b3o27b3o27b3o27b3o27b3o28b2o28b2o28b2o28b2o28b2o17bo5bo5bo
5bo5bo5bo6bo7b2o$107bo16b4o11b2o9bo6b2obo236b5o25b5o25b5o25b5o25b5o25b
5o25b5o25b5o25b5o27bobo27bobo27bobo27bobo27bobo16bo5bo5bo5bo5bo5bo7b2o
5bo$106bobo5b2o8bo2bo12bo2bo2b2o9b2ob2o3bo230b2o3b2o23b2o3b2o23b2o3b2o
23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o27b2o28b2o28b2o
28b2o28b2o55b3ob2o5b2o$104b2o3bo14b4o13bobo2bo2b3o5b2obo4b2o230b5o25b
5o25b5o25b5o25b5o25b5o25b5o25b5o25b5o214b2ob2o$99b2o3b2o3bo4bobob2o3b
4o4b2o13b4o7bobo237bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo
3bo25bo3bo214b4o$100bo3b2o3bo5b2o3bo2bo7bobo13b2o9bo239bobo27bobo27bob
o27bobo27bobo27bobo27bobo27bobo27bobo216b2o$106bobo10bo13bo265bo29bo
29bo29bo29bo29bo29bo29bo29bo198b2o8b4o$107bo8bo2bo13b2o6b2o680bo12b2ob
2o6b6o$141b3o634b2o43bo8bo3b4o7b4ob2o$143b3o255bo29bo29bo29bo29bo29bo
29bo29bo29bo135b4o46b2o2bobo3b2o12b2o$143b2o254b2ob2o25b2ob2o25b2ob2o
25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o123bo9b2ob2o31b3o2b2o
6bo2b2o3bo$126bo18bo248bo29bo29bo29bo29bo29bo29bo29bo64b2o22bo5b2o22bo
5b2o36bo11b2o34bo11b2o2bobo3b2o$127bo265bo4bo5bo18bo4bo5bo18bo4bo5bo
18bo4bo5bo18bo4bo5bo18bo4bo5bo18bo4bo5bo18bo4bo5bo23bo5bo24bobo20bobo
4bobo20bobo4bobo20b3o3bo4bo2b2o4bobo39bo8bo8bo3b4o$125b3o265b3o27b3o
27b3o27b3o27b3o27b3o27b3o27b3o64b2o20bobo5b2o20bobo5b2o25bobo3bo7bo2b
2o24b2o21bo12b2ob2o$398b2obob2o23b2obob2o23b2obob2o23b2obob2o23b2obob
2o23b2obob2o23b2obob2o23b2obob2o23b2obob2o49bo28bo33bo2bo2bo2b2o4bobo
16b4o4b4o8bo26b2o5b2o5b4o$694bo63b2o7bo11b2o9bo3bo4b2ob2o5bo3bo4b3o22b
2ob2o3bo3bo$152bo614bo9b2ob2o12bo6b2o11bo5bo22b4o8bo$131bobo4b2o11b2o
10b2o529bo82b4o9bo2bo15bo4bo4bo24b2o5bo2bo$131b2o6bo11bobo9b2o528bo59b
3o14bo7b2o30b5o$132bo6bob2o3b2o12b2o6bo3b2o212bo29bo29bo29bo29bo29bo
29bo29bo106bo39b4o5b5o13b2o16bo8bo44bo$140bo3bo3bo10b3o5bo3bobo212bobo
27bobo27bobo27bobo27bobo27bobo27bobo27bobo103b2o38bo3bo5b3ob2o11bobo
12bo3bo7b4o23b3o15b2o8b2o$149bo10b2o6b5o213b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o102bo3bo33bo7bo8b2o26bo3bo3b8obo24bo14bo9bo2bo$142bo2bo3bo
13b2o4b3o527bob2o22bo7b7o2bo2bo38bo6bo8b2o22bo16b5o4bo2bo$143bo5bo13b
2o236b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o26bobo22bo7bo2b3o
b2o34bo9b2o9bob3o41b4o3b2ob2o$144bo3bo252b2o28b2o28b2o28b2o28b2o28b2o
28b2o28b2o28b2o28b2o50b2ob2o5b7o2bo2bo29b2o13b2o5b3o45bo4b2o$146b2o
513b2o60bo2bobo9bo7bo27bobo13bo3bo33b3o$409bo29bo29bo29bo29bo132b2o55b
2o2bobo2bo13bo3bo83bo$408bo29bo29bo29bo29bo31b2o6b2o91bo57b2o4bo17b4o
53b2o27bo$159b2o247b3o27b3o27b3o27b3o27b3o28b4o4b4o148b2o78b4o49b4o$
159bo399b2ob2o3b2ob2o161bo65b2ob2o30bo2bo13bo3bo$148bobo6bobo401b2o6b
2o7b2o140bo2b2o7b2o16b4o30b2o15b2o35bo16bo$146bo3bo6b2o417b2ob2o140b3o
8bobo14bo3bo28b2ob2o47bo3bo12bo2bo$138bo7bo429b4o142bo30bo14b4o10b4o
49b4o$137b4o4bo4bo9b2o415b2o58b2o5bo2bo101bo2bo14bo3bo11b2o$125b2o9b2o
bobo4bo13bo210bo29bo29bo29bo29bo29bo30bobo81b4o8bo48bo2bo70bo$125bo9b
3obo2bo3bo3bo7bobo210bobo27bobo27bobo27bobo27bobo27bobo29b2o81b2ob2o3b
o3bo52bo44b3o18bo2bo$136b2obobo6bobo7b2o211b2o28b2o28b2o28b2o28b2o28b
2o30bo13bobo3b4o61b2o5b4o48bo3bo44bo$137b4o424bo4bo2bo2b2o109b2o9b4o
43b2o$138bo22b2o402bo3bo4bo2b2o107b2o5b3o25b2o39b2o3b2o$149bo11bobo
383bobo14bo3bo5bo2bo63b2o39b3o6b2ob2o24b4o36bo6bobo$147bo14b3o383b2o
15b2o8b2o55b2o3b3o4bo31b2o8b2o5b3o24b2ob2o34bo2bo6bo$148bo2bo11b2o199b
o29bo29bo29bo29bo63bo16b2o32b2o27b2o6b5o4b2o30b2o8b2o9b4o20b2o34b2o7b
3o$152bo7b2o201bo29bo29bo29bo29bo50b5o58b2ob2o27b3o4bob2o6bo29bo20bo3b
o2bo2bo51b2o$152bo7b3o200b3o27b3o27b3o27b3o27b3o47bo4bo28bo2bo26b4o29b
o4b2o9bo54bo6bo6b2o$151bo386bo3bobo26bo6b2o18b2o35b2o5bo2bo51bo2bo3bo
3bo4b2ob2o$533bo3bo5b2o22bo3bo4b2ob2o54b2o6bo27b5o5b2o22b4o4b4o$156bo
4b2o372bo7bo17b4o3b4o4b4o90bo4bo6b2o30b2o45b2o5b4o$157bo3bo388bo9bo3bo
12b2o65bo2bo27bo5bo77b2ob2o3bo3bo$155b3o380b2o11b2o11bo16bob2o33bobo
27bo21bo3bo33bo50b4o8bo$143b2o211bo29bo29bo29bo29bo61b2o8b3o5b2o2bo2bo
17bob2o33b2o6bo2bo14bo3bo11b2o10bo34bo3b3o46b2o5bo2bo$131b2o9bobo211bo
bo27bobo27bobo27bobo27bobo68b3o6b3o27bo32bo10bo14b4o10b4o23b2o18bo3bob
3o$131b3o10bo211b2o28b2o28b2o28b2o28b2o70b3o5b2o2bo2bo20bobo39bo3bo28b
2ob2o23b2o18bo6b2o$122b2o9b2obo11bo402b2o11bo14b2o3b2o41b4o30b2o15b2o
6bo6bo14b5obo$122bo5bo4bo2bo10b2o401bo9bo3bo13b4o21bobo70b2ob2o11bo6bo
10b4o$127bo5b2obo9b2o4b2o407b4o12bo4bo20b2o71b4o12bob2o3bo11bo$123bo3b
o3b3o11b3o4b2o424b3o23bo15b4o53b2o14b3o$125bo5b2o13b2o4b2o195bo29bo29b
o29bo139b2o28bo9bo3bo34bo35bo$147b2o6b2o191bo29bo29bo29bo142bo2b3o23b
2o11bo33b3o3b2o50b2o$148bo6bobo166b2o22b3o3b2o22b3o3b2o22b3o3b2o22b3o
3b2o28b2o28b2o28b2o28b2o15bo3bob2o18b3o5b2o2bo2bo33b5ob3o9b3o20b2o14b
2ob2o$157bo166b2o28b2o28b2o28b2o28b2o28b2o28b2o21bobo4b2o28b2o15bo3bob
o4b2o12b3o6b3o31bobo8b3o9bo3b2o18b4o13b4o$157b2o369b2o56bo5b2o13b3o5b
2o2bo2bo27b2o8b3o9bobo2b2o17b2ob2o13b2o$528bo53b4o24b2o11bo8b2o16bo10b
o9bo5bo20b2o$584bo3b2o19bo9bo3bo5b3ob2o25bo11bo2b2o$588b2o30b4o5b5o38b
o$341bo29bo29bo29bo198b3o22b2o17bo$323b3o15bobo9b3o15bobo9b3o15bobo9b
3o15bobo9b3o27b3o27b3o148b4o9bo2bo$322b2ob2o14b2o9b2ob2o14b2o9b2ob2o
14b2o9b2ob2o14b2o9b2ob2o25b2ob2o25b2ob2o147b2ob2o12bo6b2o$322b2ob2o25b
2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o140bo2bo5b2o9bo3bo4b2ob2o
$322b5o25b5o25b5o25b5o25b5o25b5o25b5o79bo29bo21b2o2bo4bo3bo16b4o4b4o$
321b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o25b2o
28b2o20bobo5b2o20bobo5b2o12bo2bo2bo2bo4b2o24b2o$532bobo27bobo20bobo4bo
bo20bobo4bobo13b2o2b3o2bo3bo$25bo308bo29bo29bo137b2o28b2o22bo5b2o22bo
5b2o14b3o2bo3bo2bo5b2o$24b2o297b2o8bo19b2o8bo19b2o8bo19b2o28b2o28b2o
28b2o137bo11b2ob2o$322b5o6b3o16b5o6b3o16b5o6b3o16b5o25b5o25b5o25b5o
147b4o$322bo29bo29bo29bo29bo29bo29bo152b2o$324b3o27b3o27b3o27b3o27b3o
27b3o27b3o$326bo29bo29bo29bo29bo29bo29bo$32bo291b2o28b2o28b2o28b2o28b
2o28b2o28b2o147b2o$31b3o290b2o28b2o28b2o28b2o28b2o28b2o28b2o146b4o$17b
o622bo11b2ob2o$16b2o11bo3bo4bobo489b2o28b2o22bo5b2o22bo5b2o14b3o2bo3bo
2bo5b2o$29bo4b2ob5o277b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o
3b2o23b2o3b2o24bobo27bobo20bobo4bobo20bobo4bobo13b2o2b3o2bo3bo$29bo2bo
bo2bo3bo277bobobobo23bobobobo23bobobobo23bobobobo23bobobobo23bobobobo
23bobobobo25b2o28b2o20bobo5b2o20bobo5b2o12bo2bo2bo2bo4b2o24b2o$34bo
285b5o25b5o25b5o25b5o5bobo17b5o5bobo17b5o5bobo17b5o79bo29bo21b2o2bo4bo
3bo16b4o4b4o$43b2o276b3o27b3o27b3o27b3o7b2o18b3o7b2o18b3o7b2o18b3o141b
o2bo5b2o9bo3bo4b2ob2o$44b2o276bo29bo29bo29bo8bo20bo8bo20bo8bo20bo149b
2ob2o12bo6b2o$44bo607b4o9bo2bo$9bo34b2o582b3o22b2o17bo$8b2o33b2o383b2o
156b2o30b4o5b5o38bo$428b2o152bo3b2o19bo9bo3bo5b3ob2o25bo11bo2b2o$44bo
413bo29bo91b4o24b2o11bo8b2o16bo10bo9bo5bo$42b3o414b2o28b2o93bo5b2o13b
3o5b2o2bo2bo27b2o8b3o9bobo2b2o$45bobo274b2o28b2o28b2o28b2o28b2o14b2o
12b2o14b2o12b2o20b3o5b2o28b2o15bo3bobo4b2o12b3o6b3o31bobo8b3o9bo3b2o$
43bo3b2o273b2o28b2o28b2o28b2o28b2o28b2o28b2o22bo5b2o28b2o15bo3bob2o18b
3o5b2o2bo2bo33b5ob3o9b3o$47bo477bo53bo2b3o23b2o11bo33b3o3b2o$577b2o28b
o9bo3bo34bo$5b3o35b3o530b3o23bo15b4o53b2o$7bo550b2o15bo4bo20b2o71b4o$
3b2ob2o446b6o31b2o50bo12b2ob2o15b4o21bobo70b2ob2o$3b3o447bo5bo28b3ob2o
49bo8bo3b4o17b2o3b2o41b4o30b2o15b2o$3b3o453bo28b5o54b2o2bobo3b2o23bobo
39bo3bo28b2ob2o$453bo4bo30b3o46b2o6bo2b2o3bo29bo32bo10bo14b4o10b4o$
455b2o77b3o10b2o2bobo3b2o20bob2o33b2o6bo2bo14bo3bo11b2o$3b3o52bo477bo
6bo8bo3b4o19bob2o33bobo27bo$2bo54b3o475bo7bo12b2ob2o81bo2bo$531bo26b2o
5b2o5b4o$55bo3bo4bobo462bo3bo29b2ob2o3bo3bo57b2o6bo$4bo3bo46bo4b2ob5o
466bo4b3o21b4o8bo20b2o35b2o5bo2bo82bo$o3bo32bo17bo2bobo2bo3bo461bo4bo
6bo22b2o5bo2bo20b4o29bo4b2o9bo79bo3bo$6bo30bo22bo9b2o458b5o5bo54b2ob2o
27b3o4bob2o6bo84bo$5b2o16b2o11bobo31bo499bo26b2o27b2o6b5o4b2o79bo4bo
20b2o5bo2bo$21b2ob2o9b3o5bo521bo3bo2bo57b2o3b3o4bo82b5o19b4o8bo$2b2ob
2o12b2o9b4o2b2o4b2o500b3o17b2o7bo65b2o108b2ob2o3bo3bo$4bo13bo3bo6bo7bo
3bo504bo18b2o6bo177b2o5b4o$19b3o8bo5bo5b2o216bo284bo20b2o4b2o$36bo5bob
o213b3o289bobo18bo64b2o5b4o$43bo213bo292bo2bo14b2o64b2ob2o3bo3bo107bob
o$43bobo16b2o193b2o375b4o8bo94bo2b2o6b2o3bo$47bo14bo488b3o81b2o5bo2bo
95bo2bobo5b3obob2o$16bo28bobo524b4o170b2o4b3o4bo$26bo18bobo506bo2bo13b
o3bo169bo9bo3bo$11bob2o6bo3b2o19b2o510bo16bo146bobo31b3o$11bobo6bob3o
23bo505bo3bo12bo2bo147b2o32bo$10bo4b2o5bo2b3o18b2o507b4o164bo$11bo8bo
2b5o18bo710bo2bo$11bo7bo7bo17bobo6b2o694b2o9bo$45bobo6bo692b3ob2o4bo3b
o$15bo31bo214bo484b5o6b4o$262b2o27b2o38b2o38b2o38b2o38b2o38b2o38b2o38b
2o38b2o38b2o38b2o31b2o22b3o$29b3o258b2ob2o35b2ob2o35b2ob2o35b2ob2o35b
2ob2o35b2ob2o35b2ob2o35b2ob2o35b2ob2o35b2ob2o35b2ob2o27b2ob2o$28bo262b
4o36b4o36b4o36b4o36b4o36b4o36b4o36b4o36b4o36b4o36b4o16b3o8b4o16b2o$
292b2o38b2o38b2o38b2o38b2o38b2o38b2o38b2o38b2o38b2o38b2o17bo11b2o15b2o
b2o$712bo27b4o$30bo3bo11b2o233bo306b2o151b2o$26bo3bo15bo234bo305b4o
119b2o$32bo247b3o304b2ob2o117bobo17b2o$31b2o556b2o15b2o103bo11b3o3b2o
9bo$604b2ob2o94b3o17b3o14b2o$28b2ob2o247b3o321b4o94b5o15bo3bo12bob2o$
30bo250bo323b2o95b3ob2o7b2o5b4o13bobo$281bo423b2o7bobo6b3o13b2o$281bo
311b2o121bo$281bo296bobo6b3o3b2o9bo$280b3o296b2o6b3o14b2o125bo2bo$579b
o6bo3bo12bob2o113b2o13bo6b2o$362b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o
12b4o13bobo113bobo9bo3bo4b2ob2o3b2o5bo2bo$220bo59b3o79bo29bo29bo29bo
29bo29bo29bo29bo14b3o13b2o116bo10b4o4b4o3b4o8bo$219bobo59bo81b3o27b3o
27b3o27b3o27b3o27b3o27b3o27b3o165b2o4b2ob2o3bo3bo$218bobobo34b2o22bo
83bo29bo29bo29bo29bo29bo29bo29bo173b2o5b4o$218bobobo34bobo335bo2bo126b
2o$219bobo37bo339bo6b2o116bobo$220bo38b2o334bo3bo4b2ob2o117bo12bo$578b
2o16b4o4b4o129bo2bo13b2o$576b2ob2o24b2o130bo3bo11b2ob2o$576b4o36b2o
112b2o5bo3bo12bo2bo$577b2o36b4o110bobo5bo3bo12bo2bo$605bo9b2ob2o111bo
6bobo3b2o9b2o$591b2o12bo11b2o120bo4b2o$590bobo8bo2b2o4bobo$592bo8bo7bo
2b2o141bo2bo$601bo2b2o4bobo146bo$605bo11b2o136bo3bo$596b2o7bo9b2ob2o3b
2o5bo2bo105b4o13b4o$595bobo17b4o3b4o8bo103bo3bo$597bo18b2o4b2ob2o3bo3b
o107bo$589b5o30b2o5b4o103bo2bo$588bo4bo$593bo7b2o$588bo3bo7bobo24b2o$
590bo11bo15b2o3b3o4bo$614b2o6b5o4b2o$615b3o4bob2o6bo$606b2o8bo4b2o9bo$
605bobo13b2o5bo2bo$607bo13b2o6bo2$630bo2bo$634bo$630bo3bo$614b4o13b4o$
613bo3bo$617bo$613bo2bo!

[calcyman]

Here's a LWSS fanout:

Code: Select all

x = 84, y = 131, rule = B3/S23
27boo$27boo7$26b3o$25bo3bo$$24bo5bo$24boo3boo3$27bo$26bobo$26bobo$22bo
3bo$19b4o3bo$11boo5b4o4bobbo$11boo5bobbo4bobbo$18b4o5boo$19b4o$22bo18$
66boo$66boo$14bo$14b3o$17bo$o15boo$3o$3bo$bboo3$16boo3boo$16boo3boo41b
oo3boo$17b5o44b3o$18bobo44bo3bo$5bo60bobo$4b3o11b3o46bo$3b5o$bboo3boo
61boo$3b5o60bo3bo$3bo3bo59bo5bo8boo$4bobo59boobo3bo8boo$5bo10bo50bo5bo
$15bo52bo3bo$15b3o52boo$3bo17bo$booboo14b3o$19b5o$o5bo11boo3boo$10boo$
ooboboo3boo$$20b3o$20b3o$$18bo4boo$16bobo4bo$17boo5b3o$26bo$3boo$3boo
4$16b4o$15bo3bo$19bo$15bobbo3$12boo$12boo$35bo$33b3o$12bo19bo$11bobo
18boo$10bo3bo$10b5o$9boo3boo$10b5o$11b3o15b3o$12bo$29bobo$16boo10b5o$
15bobo9boo3boo$17bo9boo3boo3$27boo$25boobo$25bo$$13b3o10b3obo$12bo3bo
13bo$30bo$11bo5bo$11boo3boo3$14bo10boo3boo$13bobo11b3o$13bobo10bo3bo$
15bo11bobo$15bo12bo$12bobbo$13boo$$27boo$27boo!

[Nathaniel]

Thanks for the LWSS fanout, calcyman; I dunno why I didn't think of that. Anyways, here's the last prime sequence pattern I'm going to put together, since the weeding out logic is already pretty ridiculous, and all the ideas are in place now. This gun spits out a LWSS above the honeycomb at the left edge of the pattern around generation 1620 + 120N if and only if both N and N+8 are prime. It works by splitting the prime stream into two streams, checking for N and N+8 both being prime in each stream, and then merging the resulting streams. The split is required because these prime pairs can overlap (eg. (5,13) and (11,19)). Note that the first pair, (3,11), is not detected.

This pattern can be modified to produce a stream that detects (N,N+2k) primes as long as k = 1 or 2 mod 3. If k = 0 mod 3 then it's much harder because not only can you have overlapping pairs like (5, 11) and (7, 13), but you can have "sequence" pairs like (5, 11) and (11, 17). I'm sure that the sequence pair problem can be remedied by doubling the number of streams (eg. instead of doing one split to get 2 streams, do 3 splits to get 4 streams), but I'm not going to venture down that road.

Code: Select all

#C (N,N+8) prime calculator based on the cousin prime calculator, which is based on Dean Hickerson's primer pattern
#C Created by Nathaniel Johnston on August 2, 2009 with help from calcyman
x = 1022, y = 618, rule = B3/S23
357bo13bo$356b3o11b3o$356bob2o4bo5bob2o14bo13bo$357b3o3b3o5b3o13b3o11b
3o$357b2o3b2obo5b2o13b2obo5bo4b2obo$386b3o5b3o3b3o$387b2o5bob2o3b2o2$
362bo$362b3o5b3o$363bo5bo2bo24bo$363bo2bo5bo14b3o5b3o$364b3o5bo14bo2bo
5bo$369bobo15bo5bo2bo$387bo5b3o$388bobo2$355bo$354b3o$353b2obo47bo$
353b3o47b3o$354b2o47bob2o$370bo5bo27b3o$358bobo8b3o3b3o26b2o$358b2o8b
2obo3bob2o4bo5bo$360b3o5b3o5b3o3b3o3b3o8bobo$369b2o5b2o3b2obo3bob2o8b
2o$381b3o5b3o5b3o$373bo8b2o5b2o$372b3o$364b2o20bo$365b2o5bobo10b3o$
338b3o11b3o9bo8bo20b2o$337bo2bo10bo2bo30bobo5b2o$340bo4b3o6bo31bo8bo9b
3o11b3o$340bo4bo2bo5bo50bo2bo10bo2bo$337bobo4bo3bo2bobo14b2obo2b3o28bo
6b3o4bo$344b4o20bo5bo30bo5bo2bo4bo$345bo23bo13b3o2bob2o14bobo2bo3bo4bo
bo$374bo10bo5bo20b4o$339bo33bo16bo23bo$338b3o44bo$337b2obo45bo33bo$
337b3o79b3o$338b2o79bob2o$420b3o$348b2o16bo53b2o$348b2o15b3o$365bob2o
24bo16b2o$366b3o2b2o19b3o15b2o$345b3o6b3o9b3obob2o17b2obo$319bo13bo10b
o3bo4bo2bo9b2o2bo3bo12b2o2b3o$318b3o11b3o8bo5bo6bo14b3o12b2obob3o9b3o
6b3o$317b2obo5bo4b2obo13bo7bo15bo12bo3bo2b2o9bo2bo4bo3bo$317b3o5b3o3b
3o10b4o5bobo30b3o14bo6bo5bo$318b2o4bo2b2o3b2o40bo12bo15bo7bo$324b2ob2o
45bo29bobo5b4o9b3o11b3o$323b3o2bo30b3o3b3o6bo10bo38bo2bo10bo2bo$324b2o
bo31bo2bobo2bo17bo41bo4b3o6bo$325bo33bo7bo17bo6b3o3b3o26bo4bo2bo5bo$
325bo3bo2b3o24bo7bo24bo2bobo2bo23bobo4bo3bo2bobo$326bobo3bo2bo24bobobo
bo25bo7bo30b4o$327bo4bo59bo7bo31bo$332bo20bo9bo29bobobobo$333bobo18b2o
6b3o61bo$353b2o6b2ob2o30bo9bo18b3o$362b3o30b3o6b2o18b2obo$334b3o3b3o
19b3o29b2ob2o6b2o17b3o$317bo15bo2bo3bo2bo18b3o30b3o27b2o$316b3o4b2o11b
o3bo21bobo30b3o$316bob2o16bo3bo21bobo30b3o37b2o$317b3o13bobo5bobo19bo
31bobo20bo5bo10b2o$317b2o76bobo19b3o3b3o$322b2o13b3o56bo19b2obo3bob2o
14b3o$321b3o13b3o76b3o5b3o5b3o6bo2bo$322bo2bo11b3o77b2o5b2o5bo3bo5bo$
323b2o105bo5bo4bo$421bo13bo6bobo$337b3o18bo3b3o8b2o45b3o8b4o$337b3o6bo
12b2o12bobo$326bo18b3o10b2obo3bo8b2o9b2o8b3o3bo18bobo$326b2o17bob2o35b
obo12b2o12bo7bo$325bobo8bo3bo5b3o12bo4bo17b2o8bo3bob2o10b3o$335bo5bo4b
2o12b2obo2bo44b2obo$335bo5bo9bo8b2o3b2o26bo4bo12b3o19b3o$331bo18b4o2bo
b4obo9b2o18bo2bob2o12b2o4b3ob3o8bo$331b2o17bob2o2bo7bo7bo2bo17b2o3b2o
8bo11bobo11bo$330bobo4bobo13bo5bo13b2o10b2o9bob4obo2b4o$338bo17b2o6bo
19bo2bo7bo7bo2b2obo$355bob2ob2o2b2o19b2o13bo5bo13b3o5b3o$336bo15b3o3b
4obo31bo6b2o24bo$336b2o14b3o39b2o2b2ob2obo24bo$331bo3bobo58bob4o3b3o$
330b3o72b3o$330bob2o89b3o$331b3o89bo$331b3o90bo10b3o11b3o$331b2o101bo
2bo10bo2bo$437bo4b3o6bo$437bo4bo2bo5bo$346bo87bobo4bo3bo2bobo$346b2o
92bobo2b2o$345bobo96bo$440bob2o$413b3o20bo4b3o$413bo21b3o3b3o$414bo19b
2obo$362b2o70b3o$362b2o9b2o60b2o$373bobo20b2o30bo$374b2o9b2o9b2o29b3o$
384bobo39b2obo4bo$384b2o40b3o4b3o9b2o$426b3o4bob2o14b3o$426b3o5b3o5bo
3bo4bo2bo$361bo65b2o5b2o15bo$361b2o83bo4bo$360bobo68bo15bo4bobo$430b3o
11bo2bo$398b3o28bo3bo10bo2bo$398bo30bo3bo11b2o$399bo$409bo13bo5bo3bo$
408b3o11b3o4bo3bo$408bob2o4bo5bob2o3b2ob2o$409b3o3b3o5b3o4bobo9b3o$
409b2o3b2obo5b2o6bo10bo$443bo3$414bo22b3o$414b3o5b3o12bo$415bo5bo2bo
13bo$415bo2bo5bo$416b3o5bo7bo$375bo45bobo7bo2bo$374bobo55bo$362b2o9bo
3b2o8bo45bo4bo$362b2o9bo3b2o5b4o49b3o$373bo3b2o4b4o9b2o9bo29bob2o$374b
obo6bo2bo9b2o8b3o18b3o8b3o$375bo7b4o5bo12b2obo18bo10b3o$384b4o4bo12b3o
20bo9b2o$387bo18b2o2$410bobo$410b2o$412b3o3$425bo$424b3o$416b2o6bob2o$
417b2o6b3o$416bo8b2o$392b2o$393b2o$392bo2$419b2o$419bo$417bobo$385bo
31b2o$385b2o$384bobo$375bo$374bobo$362b2o9bo3b2o8bo$362b2o9bo3b2o5b4o$
373bo3b2o4b4o9b2o$374bobo6bo2bo9b2o9b2o$375bo7b4o5bo15b2o$384b4o4bo14b
o$387bo4$400bo$400b2o$399bobo6$392b2o$393b2o$392bo2$419b2o$419bo$417bo
bo$385bo31b2o$385b2o$384bobo28bo$375bo$374bobo$362b2o9bo3b2o8bo$362b2o
9bo3b2o5b4o$373bo3b2o4b4o9b2o$374bobo6bo2bo9b2o9b2o$375bo7b4o5bo15b2o$
384b4o4bo14bo$387bo4$400bo$400b2o$399bobo6$392b2o$393b2o$392bo2$419b2o
$419bo$417bobo$385bo31b2o$385b2o$384bobo28bo$375bo$374bobo$362b2o9bo3b
2o8bo$362b2o9bo3b2o5b4o$373bo3b2o4b4o9b2o$374bobo6bo2bo9b2o9b2o$375bo
7b4o5bo15b2o$384b4o4bo14bo$387bo4$400bo$400b2o$399bobo6$392b2o$393b2o$
392bo2$419b2o$419bo$417bobo$385bo31b2o$385b2o$384bobo28bo$375bo$374bob
o$362b2o9bo3b2o8bo$362b2o9bo3b2o5b4o$373bo3b2o4b4o9b2o$374bobo6bo2bo9b
2o9b2o$375bo7b4o5bo15b2o$384b4o4bo14bo$387bo4$400bo$400b2o$399bobo6$
392b2o$393b2o$392bo2$419b2o14b2o$419bo15bobo$417bobo15bo$385bo31b2o$
385b2o$384bobo28bo$375bo$374bobo$362b2o9bo3b2o8bo$362b2o9bo3b2o5b4o$
373bo3b2o4b4o9b2o$374bobo6bo2bo9b2o9b2o$375bo7b4o5bo15b2o$384b4o4bo14b
o$387bo$480b2o$480bobo$480bo$400bo$400b2o$399bobo6$392b2o$393b2o$392bo
2$419b2o16bo87b2o$419bo15bobo87bobo$417bobo16b2o87bo$385bo31b2o$385b2o
$384bobo28bo$375bo616bo2bo$374bobo619bo$362b2o9bo3b2o8bo604bo3bo$362b
2o9bo3b2o5b4o605b4o13b4o$373bo3b2o4b4o9b2o611bo3bo$374bobo6bo2bo9b2o9b
2o604bo$375bo7b4o5bo15b2o599bo2bo$384b4o4bo14bo$387bo605bo4b2o$570b2o
413bo6bobo3b2o9b2o$570bobo410bobo5bo3bo12bo2bo$570bo413b2o5bo3bo12bo2b
o$400bo590bo3bo11b2ob2o$400b2o589bo2bo13b2o$399bobo566b3o9bo12bo$967b
5o6bobo$967b3ob2o6b2o$970b2o31b2o5b4o$995b2o4b2ob2o3bo3bo$975bo18b4o3b
4o8bo$392b2o579bobo6bo11b2ob2o3b2o5bo2bo$393b2o579b2o4b2obo3bo2bo5b2o$
392bo585b5o4bo3bo$978bo2bo4bo4b2o$419b2o194b2o353bo7b5o4bo3bo19b2o5b4o
$419bo195bobo350bobo9b2obo3bo2bo5b2o11b2ob2o3bo3bo$417bobo195bo353b2o
11bo11b2ob2o10b4o8bo$385bo31b2o575b4o12b2o5bo2bo$385b2o608b2o$384bobo
28bo599b2o$375bo623bob2o11b5o$374bobo620bo5bo10bo4bo$362b2o9bo3b2o8bo
615bo10b3o2bo$362b2o9bo3b2o5b4o609bo5bo11bo2b2o$373bo3b2o4b4o9b2o600bo
3bo2b2o9b2o$374bobo6bo2bo9b2o9b2o590b3o3b2o$375bo7b4o5bo15b2o$384b4o4b
o14bo$387bo630b4o$660b2o293bo32bo28bo3bo$660bobo290bobo30b2o12b4o17bo$
660bo293b2o31b2o10bo3bo13bo2bo$400bo602bo$400b2o597bo2bo$399bobo589bo
2bo$975bo19bo$974bobo14bo3bo$975b2o4b2o9b4o$976bo3b2o5b3o$958bo17b3o6b
2ob2o$392b2o562b2o22b2o5b3o$393b2o562b2o22b2o9b4o$392bo598bo3bo$995bo$
419b2o284b2o233bo50bo2bo$419bo285bobo230bobo$417bobo285bo233b2o40b2o$
385bo31b2o560b2ob2o$385b2o592b4o$384bobo570b2o5b4o12b2o$375bo579b2ob2o
3bo3bo$374bobo392b4o182b4o8bo$362b2o9bo3b2o8bo380bo3bo183b2o5bo2bo$
362b2o9bo3b2o5b4o384bo$373bo3b2o4b4o9b2o370bo2bo141bo47b2o$374bobo6bo
2bo9b2o384b2o127b2o32bob2o11b5o$375bo7b4o5bo388b4o127b2o29bo5bo10bo4bo
$62b4o318b4o4bo388b2ob2o163bo10b3o2bo$61bo4bo320bo384b3ob2o5b2o158bo5b
o11bo2b2o$60bobo3bo415bo267b2o19b2o5bo146bo18bo3bo2b2o9b2o$59bobo3bo
414bobo267bobo17bo7b2o143bobo19b3o3b2o$59bo421b2o267bo20b2o5bo145b2o$
24b2o33bo60b2o645bo4b3ob2o5b2o$23bobo33bo2bo57b2o2b2o640bobo12b2ob2o
178b4o$9bo12b3o4b2o29b2o56b2obo2b2o641bo13b4o149bo28bo3bo17b2o5b4o$9b
4o8b3o4bo2b4o83b3o661b2o148b2o12b4o17bo15b2ob2o3bo3bo$3b2o5b4o8b3o4b2o
b3o19b3o733b2o141b2o10bo3bo13bo2bo16b4o8bo$2bo2bo4bo2bo9bobo57b2o5bo
698b4o156bo34b2o5bo2bo$2bo2bo4b4o10b2o28bobo25b3o3bo3bo26b2o668b2ob2o
14b2o135bo2bo$5bo3b4o8bo31b5o12bo8bob2o5bo30b2o659b2o9b2o14b4o57bo50bo
17bo2bo$5bo3bo12bo29b2o3b2o11bobo6bo2bo4bo5bo20bo665bobo24b2ob2o54b2o
49b2o22bo41bo7b2o$3bobo14b3o29b2o3b2o12bobo5bob2o9b2o18b2ob2o663bo28b
2o56b2o49b2o4b2o11bo3bo32b5o7b2o3bobo$3bobo56b2o7bo2bo7b3o841bo11b4o
32bo18bo$4bo66bobo9b2o26bo5bo803bo7b2o2b3o39b3o13b3o$55bo14bobo346b2o
376b2o111bo9bo8b2o2b3o40bo4b2o$53b2o15bo9bo30b2obob2o301bo376bo2bo108b
obo10bo7b2o2b3o45b2o$b2o3b2o57bo15b2o334bobo371b3o13b2o100b2o15bo11b4o
$bo5bo21bo22bo11bo15b2o59b2o274b2o371bo2bo8bo5b2o114b2o11bo3bo$27bobo
34bo31b2o39b2o2b2o647b2ob2o3bo3bo4b2o132bo23bo26b4o$2bo3bo21b2o2b3o18b
o2bo38bo2bo38b2o2bob2o653bo4bo3bo129bo2bo22b2o26bo3bo$3b3o28bo20b2o39b
2o44b3o655bo163b2o8b4o17bo$33bo26b2o3b2o53bo5b2o799b2o44bo3bo13bo2bo$
63bo47b2o5b3o5b2o54bo625b2o115b2ob2o47bo$60bo5bo25b2o18bo4bo24b2o4bo
32bobo615b4o4b4o114b4o44bo2bo$61b2ob2o27b2o14b3o5b2o23b2o2b4o31b2obo7b
2o604bo3bo4b2ob2o11bo50bo51b2o20bo16bo2bo$62bobo27bo16bo36bo3bo18b2o
10b2ob2o6bobo607bo6b2o10b2o49b2o75b2o18bo$25b2o36bo84bo20b2o10b2obob3o
6bo602bo2bo20b2o49b2o78bo11bo3bo$4b2o18bobo36bo81bo5bo29bobo2bo2bo2bo
2bo92b2o661bo2bo11b4o$4b2o8bo11bo118bo5bo30bo4b2o6bo91b4o659bo6b2o2b3o
$14bobo129bo3bo11bo29bobo91bo2bobo188b2o413bo54bo6b2o2b3o$17b2o9b2o55b
o26b2o3b2o28b3o11bo30b2o91bobo2b2o188bobo410bobo54bo6b2o2b3o$17b2o9b2o
55b2o25b2o3b2o43bo121bobo193bo23bo29bo29bo29bo29bo29bo29bo29bo29bo29bo
29bo29bo59b2o50b3o2bo2bo11b4o8b2o$17b2o6b2o6bo3b2o24b2o19bobo92bobo
101b2o219b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o
109b3o4bo11bo3bo6bo4bo$5b2o7bobo7b3o5bo3bobo24b2o10bo38b3o8b5o35bo13b
2o67bo34b3o221bo29bo29bo29bo29bo29bo29bo29bo29bo29bo29bo29bo82bo27bo
20bo12bo$4bobo7bo10b2o6b5o36bobo37b3o7bob3obo25bo8b2o13bo65bobo35bobo
219b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o80b2o13b
4o10b3o15bo2bo7bo5bo$4bo23b2o4b3o36bo3b2o8bo27bo9bo3bo25bobo4bo3bo8b2o
59b2o6b2o33b3o3b2o632b2o11b6o8bobo28b6o$3b2o23b2o43bo3b2o5b4o38b3o26bo
2bo3bo12b2o58bo3bo4b2o12b2o19b3o650b4ob2o7b3o6b2o$73bo3b2o4b4o9b2o29bo
29bo4bobo69bo5bo3b2o12b2o18bo3bo495b2o156b2o15b2ob2o$64b2o8bobo6bo2bo
9b2o100b3o33bo3bob2o4bobo28bo5bo224b3o27b3o27b3o27b3o27b3o27b3o27b3o
27b3o27b3o26bo2bo172b4o29b4o$63bobo9bo7b4o5bo30bo23b2o48bo3bo32bo5bo7b
o29bo3bo224b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2o
b2o25b2ob2o25bo2bo173b2o19b3o7bo3bo$63bo20b4o4bo29b2o23b2o47bo5bo32bo
3bo39b3o225b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2ob2o25b2o
b2o25b2ob2o26bobo195b2o11bo$62b2o23bo33b2o4b2o68bo3bo34b2o269b5o25b5o
25b5o25b5o25b5o25b5o25b5o25b5o25b5o27b3o93b2o96b3o5b2o2bo2bo$120b3o4b
2o69b3o46bo258b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b
2o3b2o23b2o3b2o23b2o3b2o26b3o27b2o28b2o28b2o4bobo21b2o28b2o4b3o3b3o3b
3o3b3o3b3o3b3o4b3o6b3o$97b6o18b2o4b2o69b3o47b2o529bo2bo26bobo27bobo27b
obo3bo23bobo27bobo41b3o5b2o2bo2bo$96bo6bo18b2o51b2o70b2o531bobo27b2o
28b2o28b2o28b2o28b2o44b2o11bo$95bo8bo18bo50b2o333b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o29b3o192b3o7bo3bo$96bo6bo72bo330b5o25b5o25b5o25b
5o25b5o25b5o25b5o25b5o25b5o234b4o$97b6o95b2o86bo5b2o217bo29bo29bo29bo
29bo29bo29bo29bo29bo213bo2bo$188b2o8b2o57b2o18b2o5b3o5b2o213b3o27b3o
27b3o27b3o27b3o27b3o27b3o27b3o27b3o219bo$188bo2bo86bo4bo223bo29bo29bo
29bo29bo29bo29bo29bo29bo209bo7bo3bo7b6o$178bo3b3o7bo33b2o3b2o42b3o5b2o
223b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o205b3o3bo4b4o6bo5bo$177b
5o3bo6bo35b3o44bo104b2o126b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o
157b4o44b2o5b2o18bo$165b2o9b2ob2o3bo7bo34bo3bo148b2o2b2o499bo20bo3bo
43bo6b3o12bo4bo$165b2o8b3ob2o3bo3bo2bo5b2o29bobo147b2obo2b2o393b2o28b
2o22bo5b2o22bo5b2o17b2ob2o8b2o7bo32bobo9b2o5b2o14b2o$176b2ob4o5b2o7bob
o29bo148b3o127b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b2o3b2o23b
2o3b2o23b2o3b2o23b2o3b2o24bobo27bobo20bobo4bobo20bobo4bobo18b3o7b4o2bo
2bo34b2o9b3o3bo4b4o$177b4o18bo52bo255bobobobo23bobobobo23bobobobo23bob
obobo23bobobobo23bobobobo23bobobobo23bobobobo23bobobobo25b2o28b2o20bob
o5b2o20bobo5b2o27bo3b2o52bo7bo3bo2bo2bo$178bo20b2o51b2o39bo46bo160bobo
5b5o17bobo5b5o17bobo5b5o17bobo5b5o17bobo5b5o17bobo5b5o17bobo5b5o17bobo
5b5o17bobo5b5o26b2o51bo29bo36b4o2bo2bo12b2o5b4o36bo6bo6b2o$251bobo24b
2obob2o7b3o44bobo32bo4b2o120b2o7b3o18b2o7b3o18b2o7b3o18b2o7b3o18b2o7b
3o18b2o7b3o18b2o7b3o18b2o7b3o18b2o7b3o28b2o118b2o7bo9b2ob2o3bo3bo7b3o
5b2o15bo2bo3bo3bo4b2ob2o$229b2o60b5o33b2o7bob2o31b4o2b2o121bo8bo20bo8b
o20bo8bo20bo8bo20bo8bo20bo8bo20bo8bo20bo8bo20bo8bo28bobo123bo3bo9b4o8b
o6b5o5b2o22b4o4b4o$229b2o8b2o37bo5bo5b2o3b2o31bobo6b2ob2o10b2o18bo3bo
405bo124b4o10b2o5bo2bo7b3ob2o3bo33b2o$238bobo86bo6b3obob2o10b2o12bo7bo
567b2o$237bo6b2o4bo28b2ob2o43bo2bo2bo2bo2bobo22b2o5bo5bo496b2o6b5o12b
3o14b2o9bo$237bo2bo2bo2bo2bobo29bo45bo6b2o4bo24b2o4bo5bo451b2o32bo8b2o
b2o4bo4bo14bo12b5o8b3o23b2o16b3o7bo$237bo6b3obob2o10b2o28b3o33bobo41bo
3bo118bo29bo29bo29bo29bo29bo29bo29bo123bobo2bo26bobo4bo3b4o10bo13bo13b
2o4bo5bo3bo23b2o15bo9b2o$230b2o6bobo6b2ob2o10b2o28b3o34b2o42b3o117b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o123bo2b3obo3b2o19bo2bo5bo3b2o6bo3bo
28b2o5b5o4bo22bo17b3o6bob2o$229bobo7b2o7bob2o36b2o204b2o15b2o11b2o15b
2o11b2o15b2o11b2o15b2o11b2o15b2o11b2o15b2o11b2o15b2o11b2o15b2o28b2o28b
2o28b2o15bo2bobobo3b2o19bo6bo2bo12bo32b2o4b4obob2o43b3o3bobo$229bo19bo
bo36b2o65bob2o152b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o
14bo32bo2bo5bo3b2o29b3o12b3ob2o3bo51b2o$228b2o20bo34b2o6b2o60bo3bo475b
o11b3o11bobo4bo3b4o30bo18bobo30b2o$284b3o5bo2bo54bo4bo3bo475bo11bo15bo
8b2ob2o28bo53b2o$261b2o6b2o14b2o6b2o53b2ob2o4b2o470bo4bo13bo25b2o83bo$
135bo124bo2bo4bo2bo16b2o58bo4bo6bo328b4o4b4o128b2o98b4o27bo22b2o$133bo
bo124bo2bo4bo2bo16b2o58bo3b5ob3o125bobo27bobo27bobo27bobo27bobo27bobo
27bobo19bo3bo3bo3bo4bo2bo202bo2bo13bo3bo32b2o14b2ob2o$134b2o124bo2bo4b
o2bo50b3o24b3o2b2obobo126b2o28b2o28b2o28b2o28b2o28b2o28b2o24bo7bo8bo
86b2o64b3o16b2o32bo16bo31b4o13b4o$261b2o6b2o50bo3bo30bobo15b2o111bo29b
o29bo29bo29bo29bo29bo20bo2bo4bo2bo5bo3bo85bobo64bo16b2ob2o27bo3bo12bo
2bo32b2ob2o13b2o$320bo5bo29bo2bo14b2o9b2o319b4o87bo65bo15b4o16b2o11b4o
50b2o$321bo3bo31b2o26b2o296bo91b2o103b2o15b2ob2o$322b3o33bo26b2o297bo
81b4o4b4o50b2o47bo19b4o$315bo6b3o61bo295b3o80bo3bo4b2ob2o48b4o46bo20b
2o$313b3o30b2o37bobo122bo29bo29bo29bo29bo68bo4b2o63bo6b2o37bo11b2ob2o
44bobo$312bo34b2o36bobo120b2o28b2o28b2o28b2o28b2o66b4o3b2ob2o57bo2bo
44b2obo3bo2bo5b2o45bo$312b2o32bo39bo122b2o28b2o28b2o28b2o28b2o47bo16b
5o4bo2bo103b5o4bo3bo51bo15b2o3bo$323b2o354bo14bo9bo2bo55bo8bo38bo2bo4b
o4b2o24b4o36b3o4b2o$323b2o8b2o342b3o15b2o8b2o19bo2bo29bo3bo7b4o31b2o3b
5o4bo3bo24bo3bo35bo2bo5b2o$331bo2bo48b2o3b2o306bo33bo27bo3bo3b8obo29bo
bo5b2obo3bo2bo5b2o22bo35bo7b2o$330bo7b3o3bo38bobobobo276b2o58bo3bo28bo
6bo8b2o30bo7bo11b2ob2o3b2o5bo2bo3bo2bo36b2o$330bo6bo3b5o38b5o274b3ob2o
4bo24b2o5bo2bo18b4o29b2o9bob3o51b4o3b4o8bo$330bo7bo3b2ob2o9b2o27b3o83b
obo27bobo27bobo27bobo27bobo27bobo39b5o6bo22b4o8bo55b2o5b3o53b2o4b2ob2o
3bo3bo$324b2o5bo2bo3bo3b2ob3o8b2o28bo84b2o28b2o28b2o28b2o28b2o28b2o41b
3o5b3o22b2ob2o3bo3bo55bo3bo33b2o6b2o23b2o5b4o41bo2bo$323bobo7b2o5b4ob
2o125bo29bo29bo29bo29bo29bo69b2o5b2o5b4o90b3ob2o4bobo79bo6b2o$323bo18b
4o344b2ob2o29b3o22bo25b2o23b5o7bo75bo3bo4b2ob2o$322b2o20bo333b3o5bo3b
4o29bo2bo21bo25b4o23b3o35bobo47b4o4b4o$675bo2b3o3b2obo3b2o30bo4bo19b3o
6b2o15b2ob2o58b2o3bo55b2o$391bobo281bobo6bo3bo34bo32b4o16b2o11b4o23b2o
10bo8b3obob2o$390bo2bo71bo29bo29bo29bo29bo89bo2b3o3b2obo3b2o35bo27b2ob
2o27bo3bo12bo2bo6bobo19b3o4bo$389b2o10b2o60b2o28b2o28b2o28b2o28b2o93b
3o5bo3b4o30bo3bo5bo23b2o32bo16bo7bo5b2o15bo3bo$387b2o3bo8b2o61b2o28b2o
28b2o28b2o28b2o77bo26b2ob2o29bo2bo5bo54bo2bo13bo3bo12bo7bo10b3o$389b2o
5b2o266bo27b2o27bo5bo5b3o70b4o12bo3bobobo10bo$390bo2bo4bo263b3o55bob5o
24b2o70b3o$391bobo326bo4bo23b2ob2o88bo2bo$721bo3bo2b2o7b3o5bo3b4o34b3o
3b2o51bo$434b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o16b3o2bo2b
o3bo2b3o3b2obo3b2o28bo5bo3bo2b2o9b2o36bo3bo$434b2o20bobo5b2o20bobo5b2o
20bobo5b2o20bobo5b2o20bobo5b2o28b2o28b2o28b2o28b2o22bobo3bobo6bo3bo12b
o20bo3bo5bo11bo2b2o18b4o13b4o$2bo453b2o28b2o28b2o28b2o28b2o150b3o3bo2b
3o3b2obo3b2o6bo3bo16b3o9bo10b3o2bo17bo3bo$bobo380bo49bo22bo6bo22bo6bo
22bo6bo22bo6bo22bo6bo29bo29bo92b3o5bo3b4o10bo21bo5bo10bo4bo21bo$obobo
377bobo48bobo27bobo27bobo27bobo27bobo27bobo27bobo27bobo103b2ob2o4bo4bo
23bob2o11b5o18bo2bo$obobo378b2o48bobo27bobo27bobo27bobo27bobo27bobo27b
obo27bobo105b2o6b5o11bo27b2o$bobo430bo29bo29bo29bo29bo29bo29bo29bo131b
o$2bo771b3o7b4o10b2o5bo2bo$450bo29bo29bo29bo242bo3bo9b4o8bo$431b2obob
2o10b2o11b2obob2o10b2o11b2obob2o10b2o11b2obob2o10b2o11b2obob2o23b2obob
2o23b2obob2o23b2obob2o113b2o16bo7bo9b2ob2o3bo3bo$431bo5bo11b2o10bo5bo
11b2o10bo5bo11b2o10bo5bo11b2o10bo5bo23bo5bo23bo5bo23bo5bo78bo33bo2bo
10b7o2bo2bo12b2o5b4o$432bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3b
o25bo3bo26b2o28b2o20bobo5b2o21bo3bobo10bo2b3ob2o$267b4o162b3o27b3o27b
3o27b3o27b3o27b3o27b3o27b3o26bobo27bobo20bobo4bobo21bo4bo12b7o2bo2bo$
266b6o400b2o28b2o22bo5b2o22bo22bo7bo$265b8o510bo3bo$264b2o6b2o15b2o
493b4o$265b8o6bo9bobo149bobo27bobo27bobo27bobo$266b6o6bobo11bo148b2o
28b2o28b2o28b2o$267b4o7b2o4bo4bo2bo149bo29bo29bo29bo$231b2o22bobo34bo
106b2o35bo29bo29bo29bo29bo29bo29bo23bo$232bo22bo3bo22b3o4bobo107bobo
35bo29bo29bo29bo29bo29bo29bo21b3o140b4o$232bobo4bo19bo22b2o5b2o34b2o
74bo33b3o27b3o27b3o27b3o27b3o27b3o27b3o21b3o139bo3bo$233b3ob4o14bo4bo
4b2o15b2o41bobo73b2o235b2o30b2o28b2o22bo5b2o22bo22bo7bo$235b2obob2o4bo
12bo5b2o16bobo41bo342bobo27bobo20bobo4bobo21bo4bo12b7o2bo2bo$235bo2bob
3o5b2obo3bo3bo24bo42b2o203b3o136b2o28b2o20bobo5b2o21bo3bobo10bo2b3ob2o
$236bobob2o5b4obo2bobo466bo33bo2bo10b7o2bo2bo12b2o5b4o$237b4o6b2o2b2o
177b5o25b5o25b5o25b5o7bo2b2o13b5o25b5o25b5o25b5o114b2o16bo7bo9b2ob2o3b
o3bo$232b2o5bo41b2o3b2o141bob3obo23bob3obo23bob3obo23bob3obo23bob3obo
8bo14bob3obo8bo14bob3obo8bo15b5o136bo3bo9b4o8bo$91bo140b2o47b2o3b2o75b
o66bo3bo25bo3bo25bo3bo25bo3bo12bo12bo3bo7bobo15bo3bo7bobo15bo3bo7bobo
15bo3bo127b3o7b4o10b2o5bo2bo$89b3o190b5o8b3o63b3o67b3o27b3o27b3o27b3o
9bo17b3o9b2o16b3o9b2o16b3o9b2o16b3o130bo$88bo194bobo8bo3bo61bo71bo29bo
29bo29bo13bo15bo15bo13bo29bo29bo106b2o6b5o11bo27b2o$88b2o15bo187bo5bo
61bo15bo155bobo32bo178b2ob2o4bo4bo23bob2o11b5o$103b3o124b2o25bobo23b3o
8bo3bo59bo2bo13b3o190bo166b3o5bo3b4o10bo21bo5bo10bo4bo$86bo15bo155b2o
35b3o59bo16bo351b3o3bo2b3o3b2obo3b2o6bo3bo16b3o9bo10b3o2bo$85bobo14b2o
154bo36b3o58bo3bo13b2o56b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o22bobo3bobo6bo3bo12bo20bo3bo5bo11bo2b2o$84bo3bo189bo79bo73b2o28b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o16b3o2bo2bo3bo2b3o3b2obo3b2o
28bo5bo3bo2b2o9b2o$85b3o190b3o5b2o67bo5bo357bo3bo2b2o7b3o5bo3b4o34b3o
3b2o$83b2o3b2o139b2o3b2o25b3o17bo4bo68bo5bo356bo4bo23b2ob2o$230b5o25bo
3bob2o12b2o5b3o5b2o59bo3bo258bo65bo2bo29bob5o24b2o$230b2ob2o18b2o5bo3b
ob2o21bo5b2o26b2o32b3o257bo3bo37b2o28bo29bo5bo5b3o70b4o$52b2o43b2o3b2o
126b2ob2o19b2o5b3ob3o55b2o262b2o33bo37b2o15bo7bo3bo32bo2bo5bo54bo2bo
13bo3bo$52b2o43bo5bo127b3o19bo28b3o84b2o3b2o207b4ob2o27bo4bo36bo15b3o
3bo4b4o32bo3bo5bo23b2o32bo16bo$84bo197b3o85b5o208b6o29b5o52b2o5b2o42bo
27b2ob2o27bo3bo12bo2bo$84bo13bo3bo178bo3bo84b2ob2o209b4o77bo8bo6b3o37b
o32b4o16b2o11b4o$84bob3o10b3o221bo36bo9b2ob2o289b2o9b2o5b2o37bo4bo19b
3o6b2o15b2ob2o$52bo182bo9b2o33b2o3b2o35b3o46b3o290b2o9b3o3bo4b4o31bo2b
o21bo25b4o$51b3o35bo144bobo7b4o73bo3bo351bo7bo3bo2bo2bo26b3o22bo25b2o$
50bo3bo31bob2o143bob2o5b3o2bo2bobo67bob3obo33bo328bo6bo6b2o$49bob3obo
30b2o144b2ob2o9b2o2bo2bo67b5o32bobo299b3o22bo2bo3bo3bo4b2ob2o57bo3bo$
50b5o178bob2o6bo9b2o6b2o96b2o298b5o5b2o22b4o4b4o58b2o5b3o$234bobo5bo8b
o3b2o4b2o396b3ob2o5b2o30b2o21b4o29b2o9bob3o81b3o$81b2o3b2o9bo137bo6bo
10b2o33b2o372b2o5bo54bo3bo28bo6bo8b2o79b5o$81b2o3b2o9bobo150bo2bo33bob
o406bo31bo27bo3bo3b8obo80b3ob2o28b2o$82b5o7bo2b2o151bobo33b3o64b2o3b2o
14bo320bo3b3o22bo2bo29bo3bo7b4o84b2o20b4o4b4o$83bobo9bo190b2o85b3o298b
2o18bo3bob3o58bo8bo107bo3bo4b2ob2o$93b3o6bo184bobo64bo3bo7b2o4b5o298b
2o18bo6b2o178bo6b2o$83b3o15b3o184bobo2b2o60b3o8b2o3bobobobo296bo6bo14b
5obo60bo2bo111bo2bo$100b5o184bo2bobo21bo38b3o13b2o3b2o302bo6bo10b4o65b
o6b2o109bo$45bo44bo8b2o3b2o184b4o22b2o362bob2o3bo11bo63bo3bo4b2ob2o
106bo$45b2o42bo10b5o136bo49b2o14b2o2b2o4b2o42bo319b3o80b4o4b4o95b2o2bo
7bo2b2o$36b2o2b2o4b2o41b3o8bo3bo134b3o65b2o2b2o4b3o25bo14bo13bo307bo
90b2o96b4obo5bo5bo$36b2o2b2o4b3o32b2o18bobo134bo72b2o4b2o24b3o7b2o5b3o
10bobo327b2o168bo2bo6bobo2b2o$40b2o4b2o34bo19bo135b2o76b2o24bo11bo18bo
bo309b2o14b2ob2o147bo20bobo6bo3b2o$45b2o32b3o234bo25b2o7b3o20bo309b4o
13b4o147bo32b3o$45bo33bo271bo21b2o309b2ob2o13b2o148b3o$101b2o270b2o
311b2o190bo$101b2o270b2o501bo3bo7b2o$881bo5b4o$876bo4bo5b2ob2o$422bo2b
o36bo2bo36bo2bo36bo2bo36bo2bo36bo2bo36bo2bo36bo2bo36bo2bo36bo2bo36bo2b
o25bo2bo22b5o7b2o$421bo39bo39bo39bo39bo39bo39bo39bo39bo39bo39bo33bo$
421bo3bo35bo3bo35bo3bo35bo3bo35bo3bo35bo3bo35bo3bo35bo3bo35bo3bo35bo3b
o35bo3bo25bo3bo13bo2bo$421b4o36b4o36b4o36b4o36b4o36b4o36b4o36b4o36b4o
36b4o36b4o17b2o8b4o17bo$55b2o18bo765b2o26bo3bo$54bobo17bo768bo26b4o$
54bo$53b2o20bobo14b2o270b2o351b4o119bo$77bo14b2o187b2o23b2o56b2o350bo
3bo12bo2bo103b2o17b2o$70bo4bo206bo21bo2bo34bo48bo328bo16bo101bobo12bo
4b2o$70b3o3bo205bobo6bobo9bo7b5o26b3o45b3o323bo2bo13bo3bo115b3o13b3o$
73bo209b2o6bo3bo7bo6bo5bo28bo43b2ob2o340b4o94b5o15bo18bo$72b2o221bo7bo
7b2o3bo27b2o42b3ob3o436bo4bo8bo6b5o7b2o3bobo$291bo4bo7bo2bo7bo72b3ob3o
441bo8b2o14bo7b2o$295bo10b2o56b3o21b3ob3o314bo13b2o106bo3bo8bobo$92b3o
196bo3bo67b2ob2o20b3ob3o315bo7bo4b2o108bo$91bo3bo106b2o78b2o7bobo8bobo
58b2ob2o21b2ob2o314b3o6b3o13b3o126b2o5bo2bo$85b2o113bo4bo76b2o19b2o52b
2o4b5o22b3o323bo18bo114bo10b4o8bo$85b2o3bo5bo102bo6bo96bo58b2o3b2o22bo
80b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o32b5o7b2o3bobo114b2o9b2ob2o3bo
3bo12b2o$90b2o3b2o101bo8bo147bo2bo113bo29bo29bo29bo29bo29bo29bo29bo21b
o20bo7b2o114bobo11b2o5b4o3b4o4b4o$82b2o114bo8bo17b2o119b3o5bo118b3o27b
3o27b3o27b3o27b3o27b3o27b3o27b3o19bo5bo164bo3bo4b2ob2o$81bobo114bo8bo
16bobo118bo3bo6bo5bo112bo29bo29bo29bo29bo29bo29bo29bo17b3o5b2o167bo6b
2o$72b2o3b2o4bo6b2o107bo6bo16b3o4b2o112bo5bo9b2obo346bobo13b2o5bo2bo
118bo20bo2bo$74b3o12bobo108bo4bo16b3o4bo2bo77bo33bo5bo12bo361b4o8bo
117b2o$73bo3bo11bo75b2o22bo12b2o19b3o4b2o50bo28b2o20b2o370bo2bo16b2ob
2o3bo3bo116bobo$74bobo12b2o75bo20bobo34bobo54b3o26b2o20bobo15bo9bob2o
345bo17b2o5b4o130b3o13b2o$75bo17bo72bobo8b2o6b2o38b2o53b5o46b3o15b2o
11bo2bo339bo3bo157b4o13bobo$90bo2bo73b2o7bo3bo4b2o12b2o29bo48bobobobo
45b2o16b2o12bobo340b4o150bo6bo3bo12bob2o$76b3o14bo81bo5bo3b2o12b2o28bo
bo47b2o3b2o45b2o14bo2b2o393b4o111b2o6b3o14b2o$76b3o96bo3bob2o4bobo28bo
9bo3bo82b2o15bobo13bobo382bo10bo3bo110bobo6b3o3b2o9bo$175bo5bo7bo28bo
9b5o81bo2bo15bo14b2o382bobo4b2o7bo125b2o$88b2obob2o81bo3bo36bobo7b2o3b
2o48bo32b2o413b2o2bo3b4o2bo2bo$166b2o9b2o37b2ob2o7b5o48bobo78b3o363b2o
bo5bo3b2o143b2o$74b2o3b2o7bo5bo71b2o20bo26bo5bo7b3o49bobo14b2o30b2o3b
2o9b2o3b2o8bo3bo354b2o8b2o2bo3b4o2bo2bo137b4o$75b5o109b2o27bo11bo51bo
3bobo10b2o29b2o3b2o9b2o3b2o7bo5bo353b2o10bobo4b2o7bo136b2ob2o$76b3o10b
2ob2o94b2o25b2o3b2o59b2o3bo2bo8bo62bo3bo354bo5bo6bo10bo3bo12b2o107b2o
15b2o$77bo13bo189b2o6b2o11b2o28b3o13b3o11b3o361b2o17b4o3b4o4b4o104b2ob
2o$280bo2bo3bo3b2o8bobo28b3o13b3o11b3o360bobo23bo3bo4b2ob2o103b4o$166b
o114b2o6b2o9bo6b2o2b2o20bo15bo371b2o32bo6b2o105b2o$164b2ob2o117bo2bo
10bo2bo2bo2bob2o405b3ob2o27bo2bo$212bo73bobo11bo6b2o29b2o378b5o8bo$91b
2o70bo5bo22b2o3bo14b3o5b2o79bobo34b2o23b2o354b3o9b2o16bo8bo$91b2o100b
5o17bo4bo81b2o34b2o23b2o365bobo12bo3bo7b4o$163b2obob2o24b3o17b2o5b3o5b
2o107bo405bo3bo3b8obo$77b2o144bo5b2o106bobo9b2o394bo6bo8b2o$77b2o259bo
bob3o4b2o385bo9b2o9bob3o$279b2o58bob4o391b2o13b2o5b3o$184bo94bobo58bo
394bobo13bo3bo$184b2o95bo$183bobo95b2o478b2o$174bo585b4o$173bobo584b2o
b2o$172bo3b2o8bo27b2o3b2o524b2o15b2o$172bo3b2o5b4o29b3o524b2ob2o$172bo
3b2o4b4o9b2o18bo3bo523b4o$173bobo6bo2bo9b2o19bobo525b2o$174bo7b4o5bo
25bo4b2o$183b4o4bo30b2o$186bo35b2o$222bo$221bobo$222bobob3o$223bob4o$
224bo!