Mersenne Primes are the largest Prime Numbers known to man. The largest Mersenne Prime Number is 50th Mersenne prime, 2⁷⁷,232,917 − 1 (a number with 23,249,425 digits).
The evidence at hand suggests that a randomly selected Mersenne number is much more likely to be prime than an arbitrary randomly selected odd integer of similar size. Nonetheless, prime Mp appear to grow increasingly sparse as p increases. For example, eight of the first 11 primes p give rise to a Mersenne prime Mp (the correct terms on Mersenne’s original list), while Mp is prime for only 43 of the first two million prime numbers (up to 32,452,843).
The probability of finding a Mersenne Prime is “definitely” less than 0.0000647% and decreases exponentially with increase in p (Where Mp = 2^p — 1. The definition of a mersenne prime)
We have created a method of “Generating Possible Prime Numbers for Deterministic Testing” which has a relatively constant success probability of 14.188711499214312% even with possible prime numbers with billions of digits. We hope to find the first billion plus digit prime number known to mankind. But anything bigger than 23m digits works fine for a start too. We can’t even begin to explain how extraordinary achieving something like this is. And especially coming from an Indian Organization.
This is a milestone in Automatski’s Fundamental Research. And will impact the fields of Mathematics, Computer Science, Cryptography & Cryptanalysis directly. We are looking for ‘sizeable’ grants to support our research which requires human and HPC compute resources to progress from this point onwards. Let us know if this is of interest to anyone or any organization you know.
This is our website http://automatski.com