How many mersenne primes are there ?

T.Rex

How many Mersenne primes are there ?

We do not know exactly, but they are at least 43 :

The GIMPS project has found a new Mersenne prime: M43 !

$\large 2^{30,402,457} - 1$
It is the 43th known Mersenne prime and it is the new largest known prime.

It has 9,152,052 digits ! So the BIG ONE (more than 10 millions digits) is still to be found ! (and its discoverer will get about $\$$ 50,000).

Its primality has been checked 2 times: first by myself in 4 days and 21 hours using a 16x Itanium2 1.5 GHz Bull NovaScale computer, then by Jeff Gilchrist with Alpha and then Itanium2 1.6 GHz computers. Both with the http://www.oxixares.com/glucas/ Glucas program of Guillermo Ballester Valor.

The story is fully described at GIMPS (http://www.mersenne.org/ ). Read the Press Release (http://www.mersenne.org/30402457.htm).
If you read French, there is a translation: GIMPS (http://www.mersenne.org/french_prime.htm) and (http://www.mersenne.org/french_30402457.htm).

It is the second Mersenne prime found by the GIMPS project in 2005.
And we hope to find a new one before end of 2006 !

Happy New Year !

Tony

**Posted:** Sat Dec 31, 2005 11:36 am

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