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Mersenne Primes

Brief history and mathematical discovery

Joseph Fryer

on 2 December 2010

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Transcript of Mersenne Primes

Marin Mersenne (1588-1648):
-French Monk
-Mentor to young researchers
-Intrigued by perfect numbers
-Famous conjecture 1644 What are Mersenne Primes? Euclid's Formula to find
a perfect number:

If 2^(k)-1 is prime for k>1, then
n= 2^(k-1)(2^(k)-1) is a perfect number

Using Euclid's formula, Mersenne was aware that in order for 2^(k)-1 to be prime, k must also be prime.
Mersenne found prime numbers (k) that made 2^(k)-1 prime, these became known as Mersenne primes

Mersenne's conjecture: M prime for
k=2,3,5,7,13,17,19,31,67,127,257 Mersenne Primes
& Technology GIMPS Largest known prime (to date)
*seven million digits!
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