Fermat prime calculator

Fermat prime calculator
x = 838, y = 736, rule = B3/S23 46b3o12b3o$46bo2bo10bo2bo$46bo16bo$46bo3bo8bo3bo$46bo6b4o6bo$47bobobo 2b2o2bobobo$51bo6bo$51bo6bo$50bob2o2b2obo$50bo3b2o3bo$51bo6bo$51b2o4b 2o$54b2o$49bo3bo2bo3bo$53bo2bo$50b4o2b4o$52b2o2b2o$53b4o$52bo4bo2$52bo b2obo$51bo6bo$51bo6bo$53b4o$49b2obob2obob2o$48bo2b2ob2ob2o2bo$47b2o2b 8o2b2o$47bo3bo2b2o2bo3bo$46b2o5bo2bo5b2o$46b2o3b3o2b3o3b2o$47bo2b2obo 2bob2o2bo$48b2obob4obob2o$53bo2bo$48bo12bo82b3o15b3o$48bo4bo2bo4bo81bo 3bo13bo3bo$50b2o6b2o82b2o4bo11bo4b2o$44bo5b3o4b3o81bobob2ob2o3b3o3b2ob 2obobo$43b3o8b2o84b2obo4bob2ob3ob2obo4bob2o$43bob2o4bobo2bobo75bo4bo4b o3bo4bobo4bo3bo4bo$44b3o2bob2o4b2obo69b2ob3o15bo5bo$39b3o2b3o2bo10bo 67b2obo3b2o2b2o7b2o9b2o7b2o$38bo2bo4bo77b5o4bo2b2o$41bo9bo6bo61b2ob2ob obobo5bo2bo$41bo4b3o4b4o7b3o15b3o33b2obo3bo3bo8bo$38bobo4b3o15bo3bo13b o3bo28b5o4bo$45b3o14b2o4bo11bo4b2o23b2ob2obobobo3bo$48bo5b2o5bobob2ob 2o3b3o3b2ob2obobo20b2obo3bo3bo$48b2o3bo2bo3b2obo4bob2ob3ob2obo4bob2o 15b5o4bo$45bo2bo5b2o3bo4bo3bo4bobo4bo3bo4bo4bo5b2ob2obobobo3bo$48bo22b o5bo15b3o2b2obo3bo3bo$44bo3bo5b2o3b2o7b2o9b2o7b2o2b3ob3o4bo$44bo3bo4bo 2bo34b2o5bobo3bo$48bo5b2o33bo2bo6bo$45bobo42bo$54b2o52bo13bo$53bo2bo 50b3o11b3o$54b2o51bob2o4bo5bob2o14bo13bo$108b3o3b3o5b3o13b3o11b3o$54b 2o52b2o3b2o2bo4b2o13b2obo5bo4b2obo$53bo2bo58b3o19b3o5b3o3b3o$54b2o82b 2o4bo2b2o3b2o$144b3o$54b2o$53bo2bo64b3o$54b2o64bo2bo$123bo14b3o$54b2o 67bo14bo2bo$53bo2bo63bobo15bo$54b2o56b2o24bo$112b2o25bobo$54b2o92b2o$ 53bo2bo49bo41b2o$54b2o49b3o7bo$104b2obo5b2ob2o37bo$54b2o48b3o6b2ob2o 28bo7b3o$53bo2bo48b2o6b2ob2o26b2ob2o5bob2o$54b2o59b2o4bo5bo16b2ob2o6b 3o$120b3o3b3o15b2ob2o6b2o$54b2o63b2obo3bob2o4bo5bo4b2o$53bo2bo62b3o5b 3o3b3o3b3o$54b2o64b2o5b2o3b2obo3bob2o$132b3o5b3o$54b2o57b2o9bo8b2o5b2o $53bo2bo57b2o7b3o$54b2o57bo8bo3bo10bo9b2o$122bo3bo9b3o7b2o$54b2o33b3o 11b3o29bo3bo8bo$53bo2bo31bo2bo10bo2bo12b2o2bo3bo8bo3bo$54b2o35bo4b3o6b o13b2obo3bo29b3o11b3o$91bo4bo2bo5bo12bo3b2ob2o8bo3bo2b2o12bo2bo10bo2bo $54b2o32bobo4bo3bo2bobo18bobo9bo3bob2o13bo6b3o4bo$53bo2bo38bobob2o23bo 10b2ob2o3bo12bo5bo2bo4bo$54b2o40b2ob2o35bobo18bobo2bo3bo4bobo$97b3o37b o23b2obobo$54b2o34bo70b2ob2o$53bo2bo32b3o70b3o$54b2o32b2obo6bo72bo$88b 3o6b2o26bo44b3o$54b2o33b2o7bo24b2ob2o35bo6bob2o$53bo2bo38bo27b2ob2o8bo 26b2o6b3o$54b2o37b4obo18bo6b3o7b2ob2o24bo7b2o$94bo2bo18b3o15b2ob2o27bo $54b2o39b3o18bob2o15b3o6bo18bob4o$53bo2bo60b3o23b3o18bo2bo$54b2o49b3o 9b3o22b2obo18b3o$70bo13bo19bo2bo9b2o23b3o$54b2o13b3o11b3o21bo34b3o9b3o $53bo2bo11b2obo5bo4b2obo21bo35b2o9bo2bo$54b2o12b3o5b3o3b3o19bobo47bo$ 69b2o5bob2o3b2o69bo$54b2o99bobo18b3o11b3o$53bo2bo45bo7b3o3b3o56bo2bo 10bo2bo$54b2o47b2o5bo2bobo2bo59bo4b3o6bo$79bo22b2o6bo7bo24b3o3b3o7bo 18bo4bo2bo5bo$54b2o21b2o4b3o24bo7bo24bo2bobo2bo5b2o16bobo4bo3bo2bobo$ 53bo2bo26bo2bo24bobobobo25bo7bo6b2o22bobob2o$54b2o24bo2bo59bo7bo31b2ob 2o$75bo7bo30bo29bobobobo33b3o$54b2o18bo3b2o4bobo26b3o8b2o51bo$53bo2bo 17bo37b2ob2o7bobo20bo28b3o$54b2o19bo36b2ob2o8b2o9b2o8b3o26b2obo6bo$85b 3o3b3o19bobo19bobo7b2ob2o25b3o6b2o$54b2o12bo9bo5bo2bo3bo2bo19bo20b2o8b 2ob2o26b2o7bo$53bo2bo10b3o6b3o8bo3bo54bobo33bo$54b2o11bob2o5bo10bo3bo 55bo32b4obo$68b3o5bobo5bobo5bobo17b2ob2o7b2o43bo5bo5bo2bo$54b2o12b2o7b 2o28bo3bo5bo5bo2bo41b3o3b3o5b3o$53bo2bo31b3o17b2o2bo3bo7b2o10b2o7b2ob 2o17b2obo3bob2o14b3o$54b2o32b3o16b2o4b3o19bo2bo5bo5bo3bo12b3o5b3o14bo 2bo$88bobo22bobo20b2o7bo3bo2b2o14b2o5b2o15bo$54b2o33bo24bo31b3o4b2o37b o$53bo2bo32bo24bo31bobo23bo20bobo$54b2o19bo71bo23b3o$75b2o20bo49bo22bo 3bo$54b2o18bobo10bo3bo4b3o71bo3bo$53bo2bo30b2ob2o4bob2o64bo$54b2o32bob o6b3o63b3o4bo3bo11b3o$80bo16b2o63b2obo4bo3bo11bo$54b2o24b2o7bo72b3o5b 2ob2o12bo$53bo2bo22bobo7bo73b2o6bobo$54b2o33bo82bo$112bo68b3o$54b2o29b o27b2o66bo$53bo2bo28b2o25b2o35bo32bo$54b2o28bobo60b2o$148b2o$54b2o26bo 93b3o$53bo2bo24b3o6bo85bo$54b2o25bob2o5b2o32b2o51bo$82b3o4bobo22b2o8bo bo$54b2o26b3o29b2o9b2o9b2o48b3o11b3o$53bo2bo25b2o51bobo8b2o23b3o11bo2b o10bo2bo$54b2o79b2o9b2o23bo16bo4b3o6bo$172bo15bo4bo2bo5bo$54b2o129bobo 4bo6bobo$53bo2bo57bobo7b2o71bo$54b2o58bobo6bo2bo64bo4bo$113bo10b2o10b 2o7bobo43bo$54b2o57b3o19bo2bo6bobo39bo5bo$53bo2bo52b2o3b3obo17b2o10bo 37b3o3b3o$54b2o53b2o6b2o27b3o36b2obo3b3o$117b2o24bob3o3b2o20b2o10b3o4b 2o$54b2o49bo37b2o6b2o20b2o11b2o5b5o$53bo2bo48b2o36b2o34bo15b3o$54b2o 48bobo71b3o$177b2obo4bo6bo$54b2o100b3o18b3o4b3o5bo$53bo2bo99bo20b3o4bo b2o6bo7b3o$54b2o101bo19b3o5b3o6b2o6bo2bo$178b2o5b2o6b2o7bo$54b2o137bo 8bo$53bo2bo125bo20bobo$54b2o125b3o$180bo3bo$54b2o$53bo2bo$54b2o104bo 13bo5b2ob2o$113b2o5bo38b3o11b3o6bo12b3o$54b2o57b2o5b2o2b2o33bob2o4bo5b ob2o18bo$53bo2bo62bobo2bobo20b2o11b3o3b3o5b3o19bo$54b2o69b2o9b2o9b2o 11b2o3b2o2bo4b2o4bo3bo$135bobo3b3o23b3o9bobobobo$54b2o79b2o4bo38b5o5b 3o$53bo2bo85bo37b2ob2o5bo$54b2o125bobo7bo$173b3o5b3o$54b2o116bo2bo$53b o2bo118bo9b3o$54b2o119bo9bo$172bobo11bo$54b2o108b2o$53bo2bo107b2o23bo$ 54b2o132b3o$158bo24b2o3bob2o$54b2o101b3o7bo15b3o3b3o$53bo2bo99b2obo5b 2ob2o19b3o$54b2o100b3o6b2ob2o19b2o$157b2o6b2ob2o$54b2o111b2o$53bo2bo$ 54b2o2$54b2o80b2o32b3o$53bo2bo80b2o31bo$54b2o80bo28b2o4bo4bo$125b2o39b 2o7b3o$54b2o68bo3bo36bo9bob2o$53bo2bo56b2o8bo5bo7bo38b3o$54b2o57b2o8bo 3bob2o4bobo38b2o$123bo5bo3b2o12b2o21b2o$54b2o68bo3bo4b2o12b2o22b2o$53b o2bo68b2o6b2o35bo$54b2o79bobo$137bo$54b2o$53bo2bo$54b2o$151b2o$54b2o 96b2o$53bo2bo94bo$54b2o2$54b2o$53bo2bo$54b2o88bo$144b2o$54b2o87bobo$ 53bo2bo$54b2o$170b2o$54b2o114bo$53bo2bo111bobo$54b2o80b2o30b2o$137b2o$ 54b2o80bo$53bo2bo68b2o$54b2o68bo3bo$113b2o8bo5bo7bo$54b2o57b2o8bo3bob 2o4bobo$53bo2bo66bo5bo3b2o12b2o10bo$54b2o68bo3bo4b2o12b2o10b2o$125b2o 6b2o23bobo$54b2o79bobo$53bo2bo80bo$54b2o2$54b2o$53bo2bo94b2o$54b2o96b 2o$151bo$54b2o$53bo2bo$54b2o2$54b2o88bo$53bo2bo87b2o$54b2o87bobo2$54b 2o$53bo2bo113b2o$54b2o114bo$168bobo$54b2o80b2o30b2o$53bo2bo80b2o$54b2o 80bo$125b2o$54b2o68bo3bo$53bo2bo56b2o8bo5bo7bo$54b2o57b2o8bo3bob2o4bob o$123bo5bo3b2o12b2o10bo$54b2o68bo3bo4b2o12b2o10b2o$53bo2bo68b2o6b2o23b obo$54b2o79bobo$137bo$54b2o$53bo2bo$54b2o$151b2o$54b2o96b2o$53bo2bo94b 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151bo613b3o10b2o15b2o35b4o$54b2o708b5o27bo39bo$53bo2bo331b2o374b3ob2o 62bo2b3o$54b2o155bo176bobo376b2o5bo25b2o5b4o23b3o$209bobo176bo383bobo 17b2o4b2ob2o3bo3bo24bo$54b2o88bo65b2o561b2o16b4o3b4o8bo19bob3o$53bo2bo 87b2o635bo9b2ob2o3b2o5bo2bo20b2o2bo$54b2o87bobo622b2o11bo11b2o36b3o$ 768b2o7bo2b2o4bobo42bo$54b2o721bo7bo2b2o43bo$53bo2bo113b2o605bo2b2o4bo bo19b2o5b4o12bobo$54b2o114bo610bo11b2o11b2ob2o3bo3bo15bo$168bobo610bo 9b2ob2o10b4o8bo12bobo$54b2o80b2o30b2o621b4o12b2o5bo2bo15bo$53bo2bo80b 2o653b2o37bo$54b2o80bo665b2o9bo17b3o$125b2o673b5o8b3o14b2o2bo$54b2o68b o3bo304b2o365b2o4bo5bo3bo13bob3o$53bo2bo56b2o8bo5bo7bo295bobo323bo40b 2o5b5o4bo18bo$54b2o57b2o8bo3bob2o4bobo295bo323bobo42b2o4b4obob2o17b3o$ 123bo5bo3b2o12b2o10bo598b2o45b3ob2o3bo17bo2b3o$54b2o68bo3bo4b2o12b2o 10b2o650bobo22bo$53bo2bo68b2o6b2o23bobo671b4o$54b2o79bobo653bo43bo$ 137bo651b2o24b4o13b2o$54b2o734b2o22bo3bo9bob4o$53bo2bo740b4o17bo9bobo$ 54b2o740bo3bo13bo2bo9b2o$151b2o623bo23bo27b2o$54b2o96b2o620b2o20bo2bo 27bo2bo$53bo2bo94bo623b2o11bo2bo39bo$54b2o736bo38bo$478b2o300bo7bo3bo 36b3o$54b2o422bobo263bo33b3o3bo4b4o37bo$53bo2bo421bo263bobo33b2o5b2o 42b2o$54b2o88bo598b2o32bo6b3o41bobo$144b2o632b2o5b2o39bo2b2o$54b2o87bo bo632b3o3bo4b4o34bobo$53bo2bo723bo7bo3bo$54b2o736bo35b2o$788bo2bo34bo 2bo$54b2o769bo2bo$53bo2bo721b2o46b3o$54b2o80b2o593bo44b2ob2o46bo$137b 2o590b2o45b4o46b2o$54b2o80bo593b2o22b2o5b4o12b2o46bobo$53bo2bo68b2o 625b2ob2o3bo3bo58bo2b2o$54b2o68bo3bo394b2o41b4o182b4o8bo59bobo$113b2o 8bo5bo7bo385bobo39bo3bo159bo23b2o5bo2bo$54b2o57b2o8bo3bob2o4bobo385bo 45bo157bobo95b2o$53bo2bo66bo5bo3b2o12b2o416bo2bo159b2o18b2o9bo63bo2bo$ 54b2o68bo3bo4b2o12b2o430b2o165b5o8b3o60bo2bo$125b2o6b2o443b4o164b2o4bo 5bo3bo60b3o$54b2o79bobo428bo11b2ob2o163b2o5b5o4bo61bo$53bo2bo80bo426b 2obo3bo2bo5b2o166b2o4b4obob2o60b2o$54b2o506b5o4bo3bo175b3ob2o3bo61bobo $562bo2bo4bo4b2o180bobo60bo2b2o$54b2o506b5o4bo3bo245bobo$53bo2bo507b2o bo3bo2bo5b2o104bo50bo$54b2o510bo11b2ob2o101b2o49b2o24b4o57b2o$578b4o 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View static image
Pattern type	Miscellaneous
Number of cells	10001
Bounding box	838 × 736
Discovered by	Jason Summers
Year of discovery	2000
Pattern files RLE fermatprimecalculator.rle

The Fermat prime calculator is a pattern that was constructed by Jason Summers on January 7, 2000 that calculates Fermat prime numbers. In particular, it is rigged to self-destruct and stop growing if any Fermat primes over 65537 are found. Since the existence of such primes is an unsolved problem in mathematics, it is unknown if this pattern exhibits infinite growth.

The tubs that are arranged in a diagonal line at the bottom-left corner of the pattern represent the known Fermat primes, starting with 5. The other three represent 17, 257, and 65537. A tub gets destroyed whenever a Fermat prime is found. In the unlikely event that an additional Fermat prime exists, the nearby pond will eventually be destroyed, followed by the beehive puffers that border the pattern and then the breeders that make up the rest of the pattern.

A number N is tested for Fermat primality at about generation 120N - 550, so the tubs will be destroyed at about generations 50, 1490, 30290 and 7863890. The next smallest Fermat number that is not known to be composite is F₃₃, or 2^{2^33} + 1. Therefore, the pond (and the breeders) will survive at least 10^2580000000 generations, so don't expect to see anything interesting happen by watching this pattern. Remove the tubs manually if you want to see the pattern self-destruct.

The breeders each advance at c/2. Since it is impossible for a spaceship to propagate through vacuum faster than c/2, the beehive fuses are required. The small arrangement of still lifes, including the pond, triggers the beehive fuses when hit by a glider. The beehive fuses are consumed at 4c/5, hence the disturbances overtake the breeders and destroy them.

The careful observer may notice that actually every number of the form 2^N + 1 is tested for primality, while Fermat numbers are of the form 2^{2^N} + 1. However, numbers of the form M^N + 1 can never be prime unless N is a power of 2, so the only primes of the form 2^N + 1 are in fact the Fermat primes.

The Fermat prime calculator is based on the original prime number calculator, primer, and a caber tosser, both of which were found by Dean Hickerson. The beehive puffer was constructed by Hartmut Holzwart.

Image gallery

The tubs that are destroyed by the discovered Fermat primes

The calculator self-destructs and stops growing if the tubs are removed

Videos

Click to load content The Fermat prime calculator destroying the tubs representing the Fermat primes 5, 17, and 257

Trivia

• This pattern's initial population is a fermat prime in binary (0b10001 = 17).

See also

• Twin prime calculator
• Unknown fate

Further reading

• Nathaniel Johnston, Dave Greene. Conway's Game of Life: Mathematics and Construction (2022), 8.8.4. Guns and Glider Streams: Fermat Primes and Unknown Growth

External links

• Fermat prime calculator at the Life Lexicon