How does this regex find primes? [duplicate]
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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:开发者_运维知识库 primes):
/^1?$|^(11+?)\1+$/
How does this find primes?
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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