Primer

Primer
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Pattern type	Miscellaneous
Number of cells	2953
Bounding box	440 × 294
Discovered by	Dean Hickerson
Year of discovery	1991
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 only
Pattern files Plaintext primer.cells RLE primer.rle

Primer is a pattern that was constructed by Dean Hickerson on November 1, 1991 that produces a stream of lightweight spaceships representing prime numbers. N is prime if and only if a lightweight spaceship escapes to the left of the pentadecathlon at the bottom-left corner of the pattern at generation 120 N + 100. It was the first known pattern created that computes prime numbers, though others have since been constructed based on the same ideas.

It works by using gliders to emulate a prime number sieve. Lightweight spaceships that move westward are deleted by gliders that represent positive integers if the lightweight spaceship represents a multiple of that number.

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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2obo5bo129b4o5b5o13b2o16bo$289bo3bo5b3ob2o11bobo12bo3bo62b2o$293bo8b2o 26bo3bo9bo52bo2bo$285bo6bo38bo12b6o42b2o3bo2bo$152b2o6bo88bo29bo7b3o 32bo9b2o9bob3o44bo3b2ob2o$152bo6b3o86b2o28b2o5bo6bo29b2o13b2o9bo48b2o$ 159bob2o130bo27bobo13bo37b3o$160b3o126bo3bo83bo$107b2o6b2o43b2o128b4o 53b2o27bo$106b4o4b4o228b4o49b4o$106b2ob2o3b2ob2o227b2ob2o33bo13bo3bo$ 108b2o6b2o7b2o47b3o120b4o30b2o15b2o35bo16bo$123b2ob2o46bo2bo118bo3bo 28b2ob2o47bo3bo15bo$123b4o16b3o28bo125bo14b4o10b4o49b4o$124b2o16bo2bo 28bo9b2o8bo104bo14bo3bo11b2o$145bo28bo8b4o8bo51bo70bo$145bo29bo7b2ob2o 3bo3bo52bo68bo$120b4o20bo40b2o5b4o48bo3bo$116b2o2bo2b2o120b4o$117bo3bo 2b2o114b3o25b2o39b2o3b2o$121bo2bo113b2ob2o24b4o36bo6bobo$122b2o67bo31b 2o15b3o24b2ob2o34bo2bo6bo$146b2o44b2o30b2o19b4o20b2o34b2o7b3o$81b5o58b 2ob2o44bo29bo20bo3bo5bo51b2o$80bo4bo31bo26b4o13b3o29bo54bo6bo6b2o$85bo 32bo6b2o18b2o7bo6bo2bo27bo54bo3bo3bo4b2ob2o$84bo29bo3bo4b2ob2o24bobo6b o56b5o29b4o4b4o$108b4o3b4o4b4o26b2o6bo55bo4bo38b2o45b2o5b4o$107bo3bo 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 $160b2o2bo2bo27b2o20bobo2b2o$160b3o31bobo20bo3b2o$160b2o2bo2bo51b3o$ 168bo$164bo3bo31bo$165b4o31b2o20b2o$105b2o92bobo19b4o$b6o31b2o63b2ob2o 113b2ob2o$o5bo28b3ob2o58bo3b4o65b4o30b2o15b2o$6bo28b5o54b2o2bobo3b2o 65bo3bo28b2ob2o$5bo30b3o54bo2b2o3bo73bo14b4o10b4o$94b2o2bobo3b2o68bo 14bo3bo11b2o$99bo3b4o86bo$103b2ob2o84bo$105b2o5b2o5b4o28b2o$80bo29b2ob 2o3bo3bo27bobo$81bo28b4o8bo20b2o7bo37bo$76bo4bo29b2o8bo20b4o45bo83bo$ 77b5o60b2ob2o44bo84bo$144b2o44b2o79bo4bo20b2o8bo$119bo69bo82b5o19b4o8b o$120bo175b2ob2o3bo3bo$115bo4bo177b2o5b4o$114b2o3b2o$118bo64b2o5b4o$ 181b2ob2o3bo3bo90bobo14bobo$181b4o8bo90b2o5b2o6b2o3bo$182b2o8bo92bo5bo bo5b3obob2o$119b4o170b2o4b3o4bo$104bo13bo3bo169bo9bo3bo$105bo16bo180b 3o$101bo3bo15bo181bo$102b4o$307bo$297b2o9bo$294b3ob2o4bo3bo$294b5o6b4o $271b2o22b3o$269b2ob2o$269b4o16b2o$270b2o15b2ob2o$287b4o$135b2o151b2o$ 134b4o$127bobo4b2ob2o$136b2o15b2o132bo$128bo22b2ob2o94b3o34b2o$128bo 22b4o94b5o32bob2o$128bo23b2o95b3ob2o31bobo$252b2o32b2o2$128bo22bo$128b o22b2o128bo$128bo21bob2o113b2o13bo6b2o$150bobo113bobo9bo3bo4b2ob2o3b2o 8bo$127bobo20b2o116bo10b4o4b4o3b4o8bo$288b2o4b2ob2o3bo3bo$296b2o5b4o$ 145bo126b2o$146bo6b2o116bobo$142bo3bo4b2ob2o117bo$125b2o16b4o4b4o146b 2o$123b2ob2o24b2o146b2ob2o$123b4o36b2o112b2o22bo2bo$124b2o36b4o110bobo 22bo2bo$162b2ob2o111bo23b2o$164b2o$157bobo$156bo2b2o121b2o21bo$157bobo 121bobo22bo$164b2o117bo3bo14bo3bo$162b2ob2o3b2o8bo105bo3bo12b4o$162b4o 3b4o8bo104bo2b2o$163b2o4b2ob2o3bo3bo109bo$136b5o30b2o5b4o105b2o$135bo 4bo$140bo$139bo$177bo$178b2o$179bo$179bo$178bo3$180bo$181bo$177bo3bo$ 161b4o13b4o$160bo3bo$164bo$163bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 640 WIDTH 960 THUMBSIZE 2 ZOOM 2 ]]

The pattern (click above to open LifeViewer) RLE: here Plaintext: here

Image gallery

The stream of spaceships representing prime numbers

Videos

Click to load content Primer outputting the prime numbers from 2 through 37

See also

• Fermat prime calculator
• tlog(t) growth
• Twin prime calculator

External links

• Primer at the Life Lexicon
• Prime Number Calculators at Game of Life News. Posted by Dave Greene on December 15, 2007.
• Prime numbers at Game of Life News. Posted by Adam P. Goucher on February 04, 2010.