Team South Africa

On April 12th, the 47th known Mersenne prime, 2^42,643,801-1, a 12,837,064 digit number was found by Odd Magnar Strindmo from Melhus, Norway! This prime is the second largest known prime number, a "mere" 141,125 digits smaller than the Mersenne prime found last August.

Odd is an IT professional whose computers have been working with GIMPS since 1996 testing over 1400 candidates. This calculation took 29 days on a 3.0 GHz Intel Core2 processor.

The prime was independently verified June 12th by Tony Reix of Bull SAS in Grenoble, France using the Glucas program running on Bull NovaScale HPC servers, one featuring Itanium2 CPUs and another featuring Nehalem EX CPUs.

Perfectly Scientific, Dr. Crandall's company which developed the FFT algorithm used by GIMPS, makes souvenir posters you can order. You'll need a good magnifying glass to read all 12.8 million digits!

Chris Caldwell maintains an excellent web site on prime numbers. See his page on Mersenne Primes and their history.

This is the 13th Mersenne prime found by GIMPS in its 13 year history.

This is incredible! And so soon too.

I just went to the GIMPS website and find this of particular interest:
M44 was discovered in September 2006...
M45 & M46 were discovered in August/September 2008... (2 years later after M44).
M47 has been discovered now in June 2009... (8 months after M45 & M46).

I'm guessing that the decrease in times between discoveries can be directly attributed to Moore's Law. I wonder though... does this mean that we can expect M48 to be discovered within the next 6 months?

By the way, Chris Caldwell's pages can found here.

stackoverflow wrote:This is incredible! And so soon too.

I just went to the GIMPS website and find this of particular interest:
M44 was discovered in September 2006...
M45 & M46 were discovered in August/September 2008... (2 years later after M44).
M47 has been discovered now in June 2009... (8 months after M45 & M46).

I'm guessing that the decrease in times between discoveries can be directly attributed to Moore's Law. I wonder though... does this mean that we can expect M48 to be discovered within the next 6 months?

By the way, Chris Caldwell's pages can found here.

The distribution of primes is random, if the "experts" are to be believed. The discovery of the latest Mersenne Prime was announced and discussed in some detail here. On the 4th page there's quite a bit of discussion about the distribution of primes. It seems that it is something of a coincidence. It's also interesting to note that the prime was actually discovered in April and nobody noticed until now!

Certainly, Moore's law helps to get the crunching done quicker than would otherwise have been the case, but the amount of work needed as the numbers get bigger goes up dramatically. The next big target is a prime with 100 million digits. This will, with modern PC's take something like 5 years to test just one number in the hope it may be prime! In that time, technology will have moved on quite a bit and the computer doing the work will likely have died of exhaustion. Most would agree that it's better to wait until the technology catches up. In any case, there are many tests to be conducted on much smaller numbers.

Warped wrote:The next big target is a prime with 100 million digits. This will, with modern PC's take something like 5 years to test just one number in the hope it may be prime!

Good grief!!! So a machine running that long would probably have to run during the hot summer too, and therefore need a sophisticated cooling system?

Warped wrote:In that time, technology will have moved on quite a bit and the computer doing the work will likely have died of exhaustion. Most would agree that it's better to wait until the technology catches up. In any case, there are many tests to be conducted on much smaller numbers.

Perhaps, but that would require waiting a long time would it not? Is it not possible to break up workunits so that multiple machines work on a single number? This would introduce other problems, like having to wait for machines to finish before results can be collated, but I'd imagine that it would allow us to go in search of that elusive 100 million digit number.