Primer

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 120N+100.[1][2] It was the first pattern created that computes prime numbers, though others have since been constructed using the same ideas (see glider gunless primer).

Primer
<html><div class="rle"><div class="codebox"><div style="display:none;"><code></html>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 b2o$76b2o3b2o2bo4b2o49b2obo5bo4b2obo244bo13b4o16b2o$81bo3bo24b3o28b3o 5b3o3b3o245b3o11b2ob2o$81bob2o57b2o4bo2b2o3b2o261b2o$81b2o38b3o24bo3bo $149b2obo213bo$75b3o73b2o214b2o42b2o$74bo2bo288b2o41b2ob2o$77bo78b3o 250b4o$77bo78bo2bo246bo3b2o$76bo79bo248b2o$156bo249bo3b2o$102b3o52bo 251b4o$102bo2bo303b2ob2o$102bo26b3o279b2o$92bo9bo25bo2bo227bo$91b3o8bo 28bo226bo$55b3o11b3o19bob2o8bo27bo9bo216b3o36b4o$54bo2bo10bo2bo20b3o 36bo8b3o253bo3bo$57bo4b3o6bo20b2o36bo8b2obo239b2o16bo$57bo4bo2bo5bo67b 3o209bo21b4o4b4o14bo$56bo4bo8bo69b2o21bo13bo9b2o163b2o18bo3bo4b2ob2o$ 97bo5bo58b3o11b3o7b4o161b2o23bo6b2o$96b3o3b3o57bob2o4bo5bob2o6b2ob2o 184bo$62b2o31b2obo3bob2o4b2o18bo5bo26b3o3b3o5b3o8b2o189bo$62bo7bo24b3o 5b3o4bobo16b3o3b3o25b2o3b2o2bo4b2o198bo$69b3o24b2o5b2o6b2o9b2o4b2obo3b ob2o29bo3bo28bo175bo2b2o$68b2obo49bobo4b3o5b3o29bob2o30bo173bo5bo$68b 3o29bo20b2o6b2o5b2o30b2o28bo3bo174bobo2b2o$69b2o28b3o97b4o174bo3b2o$ 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4bo164b4o12bo15bo4bo29b2o8bo$145bo5bo2bo4bo140b3o14bo7b2o30b5o$146bo4b 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 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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 ]] <nowiki></nowiki> <html></code></div></div><canvas width="200" height="300" style="margin-left:1px;"><noscript></html> <html></noscript></canvas></div></html>
View static image
Pattern type Miscellaneous
Number of cells 2953
Bounding box 440×294
Discovered by Dean Hickerson
Year of discovery 1991

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.

The stream of spaceships representing prime numbers

Videos
<iframe src='//www.youtube.com/embed/68nEX5CEmZE?' width='300' height='169' frameborder='0' allowfullscreen='true'></iframe>
Primer outputting the prime numbers from 2 through 37
gollark: What do you mean "arbitrary polls"?
gollark: I have been accused of this. But never actually diagnosed, so things.
gollark: Oh no. I didn't plan for this.
gollark: That's very mean to my alts and I want you to apologize IMMEDIATELY.
gollark: My ~26 alts all asked invisibly.

See also

References
  1. PRIMES.LIF from Alan Hensel's lifep.zip pattern collection. Accessed on July 28, 2009.
  2. four-primers.rle.gz from Golly's built-in pattern catalogue. Accessed on July 28, 2009.
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