Twin prime calculator

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Twin prime calculator
x = 440, y = 294, rule = B3/S23 412b2o$410b2ob2o13b2o$410b4o13b4o$411b2o14b2ob2o$93b3o11b3o319b2o$93bo 2bo10bo2bo$93bo6b3o4bo16b3o11b3o$93bo5bo2bo4bo15bo2bo10bo2bo$94bo4b2ob o5bo17bo4b3o6bo285b2o$126bo4bo2bo5bo284bo2bo$125bo5bob2o4bo285bo2b2o$ 424bo2b2o$99bo8bo315b4o$99bobo5b3o278bo7bo$107bob2o14bo8bo254bo7b2o$ 100bo2bo4b3o13b3o5bobo249bo4bo6b2o30b2o$101b3o4b2o13b2obo258b5o29b4o4b 4o$102bo20b3o4bo2bo280bo3bo3bo4b2ob2o$124b2o4b3o282bo6bo6b2o$131bo279b o3bo5bo$412b4o$91b3o313b3o$90bo2bo311b2ob2o26b2o$93bo46b3o264b3o17b4o 4b4o$93bo46bo2bo268b4o10bo3bo4b2ob2o$92bo47bo270bo3bo14bo6b2o$106b3o3b 3o25bo274bo13bo$105bo2bo3bo2bo25bo272bo18bo$108bo3bo6b3o3b3o253bo49bo$ 96b3o9bo3bo5bo2bo3bo2bo253b2o47bo2b2o$98bo8bo5bo7bo3bo255b2o47bo5bo$ 97bo12bo10bo3bo9b3o293bobo2b2o$110bo9bo5bo8bo295bo3b2o$109bobo11bo12bo 296b3o$101b3o19bo$76bo13bo12bo18bobo$75b3o11b3o10bo27b3o303b2o$75bob2o 4bo5bob2o37bo12bo13bo277b4o$76b3o3b3o5b3o38bo10b3o11b3o245bo13b2o15b2o 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12b2o36bo31bo27bo83b2ob2o3bo3bo$111bo83bo25bo33bo50b4o8bo$103b2o2bo2bo 65bo14bo3bo11b2o45bo3b3o46b2o8bo$103b3o71bo14b4o10b4o43bo3bob3o$103b2o 2bo2bo62bo3bo28b2ob2o43bo6b2o$111bo62b4o30b2o15b2o28b5obo$107bo3bo111b 2ob2o29b4o$108b4o89bobo19b4o31bo$167b4o31b2o20b2o12b2o$166bo3bo31bo36b 2o$170bo67bo23b2o$162b2o2bo2bo51b3o20b2o14b2ob2o$162b3o31bobo20bo3b2o 18b4o13b4o$162b2o2bo2bo27b2o20bobo2b2o17b2ob2o13b2o$170bo8b2o16bo20bo 5bo20b2o$166bo3bo5b3ob2o37bo2b2o$167b4o5b5o38bo$177b3o22b2o17bo$201b4o 12bo$201b2ob2o12bo6b2o$194bo2bo5b2o9bo3bo4b2ob2o$185b2o2bo4bo3bo16b4o 4b4o$170b2o12bo2bo2bo2bo4b2o24b2o$169bobo13b2o2b3o2bo3bo$156b2o11b2o 14b3o2bo3bo2bo5b2o$155bobo31bo11b2ob2o$157bo43b4o$202b2o3$200b2o$155bo 43b4o$153bobo31bo11b2ob2o$154b2o11b2o14b3o2bo3bo2bo5b2o$167bobo13b2o2b 3o2bo3bo$168b2o12bo2bo2bo2bo4b2o24b2o$183b2o2bo4bo3bo16b4o4b4o$192bo2b o5b2o9bo3bo4b2ob2o$199b2ob2o12bo6b2o$199b4o12bo$103bo71b3o22b2o17bo$ 103b2o60b4o5b5o38bo$102bobo59bo3bo5b3ob2o37bo2b2o$168bo8b2o16bo20bo5bo 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Pattern type Miscellaneous
Number of cells 3062
Bounding box 440×294
Discovered by Dean Hickerson
Year of discovery 1994

The twin prime calculator is a pattern that was constructed by Dean Hickerson on September 9, 1994 that produces a stream of lightweight spaceships representing twin prime numbers (except for the pair (3, 5)). In particular, N and N+2 are both prime if and only if a lightweight spaceship escapes past the gun at the bottom-left corner at about generation 120N+540.[1][2] It works by attaching a period 240 glider gun to the bottom-left corner of Hickerson's original prime number calculator, primer, which allows a lightweight spaceship to pass by it if and only if another lightweight spaceship tried to pass by 240 generations earlier.

By having various guns pointed at the output stream of of primer, it is possible to similarly construct various other prime-generating patterns. For example, a prime quadruplet calculator and a cousin prime calculator have both been constructed.[3]

Videos

The twin prime calculator outputting four lightweight spaceships that represent the four twin prime pairs (5,7), (11,13), (17,19), and (29,31)

See also

References

  1. Jason Summers' pattern collections. Retrieved on July 28, 2009.
  2. twinprimes.rle from Golly's built-in pattern catalogue. Retrieved on July 28, 2009.
  3. Nathaniel Johnston. "Prime quadruplet calculator". ConwayLife.com forums. Retrieved on July 29, 2009.