Editing MersennePrime
You are currently browsing as guest..
To change this, fill in the following fields:
Username
Password
Click here to reset your password
Who can read this page?
The World
Members
Council
Admin
You have been granted an edit lock on this page
until Sat Apr 27 02:04:04 2024.
Press
to finish editing.
Who can edit this page?
World editing disabled
Members
Council
Admin
A Mersenne number is a number of the form EQN:M_n=2^n-1. Mersenne numbers which are also prime are called Mersenne Primes. Most of the largest primes known are Mersenne Primes as there exists an efficient method of testing the primality of such numbers called the Lucas-Lehmer test. There exists an International Project to find unknown Mersenne primes called the Great Internet Mersenne Prime Search (GIMPS) where volunteers allow the down-time on their computers to be used for the endeavour. EQN:M_p=2^p-1 is known to be prime for 47 values of p = 2, 3, 5, 7, ... , 43112609 EQN:2^{43112609}-1 is the largest known prime number, was discovered in August 2008 and is 12,978,189 digits long. ---- Enrichment Task Show that if /n/ /(=ab)/ is a composite number then EQN:2^a-1 is a factor of EQN:2^n-1 therefore if EQN:2^n-1 is prime then /n/ is prime. ---- See also: Fermat prime.