maxprime

Introduction:

• Get the maximum prime in [3, 3,317,044,064,679,887,385,961,980] at an incredible speed(about several ms).

• My first program,I didn't even know how to print "Hello World!" at that time.

• I keep the code as it was for reminding me "Never forget why you started".

Math

Here is an article written by me.

And Here is another one.

And my steps to get things done:

1. I found I could make Fermat's little theorem being "stronger", and that's called Miller–Rabin primality test.
2. Then I used Prime number theorem to get close to the prime.
3. I developed a mod algorithm named it "sexy_mod", now I know it's Montgomery reduction :D
4. Done.

Usage

(max_prime <Number>)

e.g.

(max_prime 3317044064679887385961980)

Result: 3317044064679887385961813

It will cost about 30ms.