Mersenne Prime Search

My attempt to generate and verify arbitrarily large Mersenne primes.

Current largest:

M(859433) == 2^859433 - 1 with 258716 digits (Pure Python3)

Mersenne primes:

From Wikipedia, the free encyclopedia

Largest known term 2^77,232,917 − 1 (December 2017)

OEIS index A000668

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.

The Algorithms:

Miller–Rabin primality test

Lucas–Lehmer primality test

How to Run

• git clone https://github.com/vishnuvardhan-kumar/mersenne-prime-search.git

• cd mersenne-prime-search

• python mersenne.py

Project Roadmap

• Move from Python3 to C/C++ (using a library such as GMP)
• Parellize operations on threads/microthreads
• Implement prime exponent paradigm