第45個梅森質數

以下資料請參考，更進一步資料請參考

http://www.mersenne.org/
http://www.equn.com/gimps/

http://primes.utm.edu/notes/M45_46.html

GIMPS found two new primes: 2^43112609-1 (about 12.9 million digits, Aug 08) and 2^37156667-1 (only 11.1 million digits, Sept 08).

It had been about two years since GIMPS had found a prime and also two years longer than we had expected to wait for a 10,000,000 digit prime... Part of the reason for the anticipation was that such a prime would win the $100,000 prize from the Electronic Fronteir Foundation. So we waited...

Edson Smith had spent the last 10 years serving as Computing Manager for the UCLA Mathematics department. He decided to change some of the departments screen savers to something more productive, and placed the GIMPS software on these machines. On August 23rd 2008, one of them found the 45th known Mersenne

2^43,112,609-1 (12,978,189 digits).
Edson calls it the UCLA Mersenne prime in his excellent FAQ.

It takes a lot of work to verify such a behemouth, and as that work was being completed, lightening struck again! On September 6th 2008, Hans-Michael Elvenich (who runs www.primzahlen.de) in Langenfeld Germany found

2^37,156,667-1 (11,185,272 digits),
also as part of the GIMPS project.

Lightening struck twice at UCLA as well, in fact eight times! In 1952, Professor Raphael Robinson found five Mersennes, and in 1961, Professor Alexander Hurwitz found two more.

Some have asked if lightening also struck twice in another way--are these primes surpisingly close together? Probably not. We know a fair amount about the Mersennes, though not enough yet to prove there are infinitely any of them. However there is a heuristic argment that they should follow a simple pattern, and the gaps between the log of the log of these primes follow very closely to what is expected.