Use Fermat's Little Theorem to check if a number if prime. #1

paterson · 2014-05-06T16:09:54Z

Hey there :)

Using Fermat's Little Theorem is a much much more efficient way of checking if a number is prime than the way you were doing it. This should make prime checking, and prime generation a lot faster.

Fermat's Little Theorem is as follows:

In Ruby thats:

a ** p % p == a

I ran numerous benchmarks on my machine (MacBook Pro):

https://gist.github.com/paterson/18493006a7c673e8beaa

(Results are in gist).

Anyway I was studying and got kinda bored. Should help, it's not always that one line pull request can make an up to 90000% speed improvement :)

Using Fermat's Little Theorem is a much more efficient way of checking if a number is prime (200-300% for ~500 numbers generation. Significant increase at ~10000). This should make prime checking, and prime generation a lot faster.

paterson · 2014-05-06T17:13:59Z

WIP. Don't merge yet. Thanks!

jihyeseo · 2017-08-30T05:49:26Z

An intriguing thought!
Any prime number p satisfies the equation, but there are p which are not prime, but still satisfies the same equation.
https://en.m.wikipedia.org/wiki/Carmichael_number

Update one_liner.rb

70b4da6

Using Fermat's Little Theorem is a much more efficient way of checking if a number is prime (200-300% for ~500 numbers generation. Significant increase at ~10000). This should make prime checking, and prime generation a lot faster.

paterson changed the title ~~Update one_liner.rb~~ Use Fermat's Little Theorem to check if a number if prime. May 6, 2014

paterson changed the title ~~Use Fermat's Little Theorem to check if a number if prime.~~ Use Fermat's Little Theorem to check if a number if prime. This increases performance by up to 90,000% May 6, 2014

paterson changed the title ~~Use Fermat's Little Theorem to check if a number if prime. This increases performance by up to 90,000%~~ Use Fermat's Little Theorem to check if a number if prime. May 6, 2014

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Use Fermat's Little Theorem to check if a number if prime. #1

Use Fermat's Little Theorem to check if a number if prime. #1

paterson commented May 6, 2014

paterson commented May 6, 2014

jihyeseo commented Aug 30, 2017

Use Fermat's Little Theorem to check if a number if prime. #1

Are you sure you want to change the base?

Use Fermat's Little Theorem to check if a number if prime. #1

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paterson commented May 6, 2014

paterson commented May 6, 2014

jihyeseo commented Aug 30, 2017