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How to determine if a number is a prime with regex?
This page claims that this regular expression discovers non-prime numbers (and by counter-example: primes):
/^1?$|^(11+?)\1+$/
How does this find primes?
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15This is **not** a dup. It's a different regexp and a different technique, and has better answers, to boot. – bmargulies Jul 22 '10 at 22:03
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4@bmargulies: This *is* a dupe. The regex is the same, given the input restrictions on this question and that Java's String.matches method matches the regex against the entire string (so ^ and $ are implied), which it apparently does. – Jul 22 '10 at 22:57
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1@Rog - the upvoted answers over there never mention unary. – bmargulies Jul 22 '10 at 23:33
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@bmargulies: If you believe you can provide a better or more complete answer to that question, please, do so. I'd flag this question for merging, but the *superficial* differences in question text mean the answers need some editing (as is often the case), even though the questions are identical once you remove those superficial differences. – Jul 23 '10 at 04:43
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@Rog at this point I'll just trust the diamonds to merge cleverly. – bmargulies Jul 23 '10 at 11:08
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`^(?!1?$|(11+?)\1+$)1+$` will find the actual primes, using a negative lookahead – Wilson Jul 14 '23 at 21:32
1 Answers
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I think the article explains it rather well, but I'll try my hand at it as well.
Input is in unary form. 1 is 1, 2 is 11, 3 is 111, etc. Zero is an empty string.
The first part of the regex matches 0 and 1 as non-prime. The second is where the magic kicks in.
(11+?) starts by finding divisors. It starts by being defined as 11, or 2. \1 is a variable referring to that previously captured match, so \1+ determines if the number is divisible by that divisor. (111111 starts by assigning the variable to 11, and then determines that the remaining 1111 is 11 repeated, so 6 is divisible by 2.)
If the number is not divisible by two, the regex engine increments the divisor. (11+?) becomes 111, and we try again. If at any point the regex matches, the number has a divisor that yields no remainder, and so the number cannot be prime.
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Might be easier to follow: this is how the same regex would be written in [kleenexp](https://github.com/SonOfLilit/kleenexp) syntax: `[#start_line [ | '1' | [capture:factor 1+ '11'] [1+ #repeat:factor] ] #end_line]` – Aur Saraf Sep 01 '22 at 22:58
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