Mersenne Prime

«Fermat»

Filled all bits by value 1, and undivided by any other integer, the number is a Mersenne prime.

Why is that named Mersenne? the erudite monk, only with pens and papers repeatedly counting off and checking on, felt in this kind of happiness.

Now, by fast computing of computers, everyone is busy breaking the world record for the largest known primes.

How to find? Lucas-Lehmer simple sequence is the current adoption; however, to see through it, you have to know many mathematicians.

Euler

Our site provides one new equation with simple proving; as long as heard about two ancestors, Fermat and Euler, you may easily understand hereof.

If b_c= b₁ (mod M_c), where b_k+1= (b_k)² -2, b₀= -(1/3 +3) (mod M_c), then M_c is a prime.