Göran Axelsson's Prime Number Page.

I have always been interested in mathematics and as soon as I got my first computer (a Sinclair QL) I started to calculate prime numbers. At a beginning it wasn't so effective and I didn't know anything beyond "The sieve of Erasthones". I stayed at this level for a long time. It wasn't until I came to the university to study technical physics in 1990 that I learned about some more fancy algorithms as Lucas-Lehmer's test for Mersenne numbers. It didn't take me long time until my 386 was running around the clock. With the new Linux OS (1992) it even didn't affect the other programs I was running. At that time I was still ignorant about any coordinated searches. During this time I discovered some nice algorithms for modulo calculations. Of course it was already known but I did it by my self. I got really dissapointed the day when a friend sat down and wrote a mersenne program that beat my program by a factor of ten. OK, it didn't last long and a couple of days later I too were using GMP (Gnu Multi Precision) and the numbers just flew away. In 1998 I found out about GIMPS and realised that I had only checked mersenne numbers already tested.... the only sensible thing to do was to drop my old program and join. Around this time I also found out about Proth and started toying around with it. I didn't discover any new primes and soon other interests took over. I stayed with GIMPS and started to learn about number theory. I joined a course on the university and tried to develop some new algorithms without any sucess. During this time I also made some trials to factorise some Fermat numbers but the only thing I got out of it was a better theoretical base to continue my studies on. Then during the spring of 2001 we got a new Athlon on the job and I found that it was very fast for running Proth, so I reserved some ranges and started it. Finally!!! A nice primenumber with 32633 digits appeared and I managed to get in on the top 5000 list. Too bad that the computer should be used in a lab and I had to leave it. Then during the summer we got a new P4-1.5GHz and I just had to test it out on Proth. Wooooo! Fassst! Then at the same time I heard about the programs PRP and NewPGen and toyed around with it for a while. Then I searched for a good interval to try it out and I struck gold on the first trial. A quick search on the top 5000 list revealed that it already existed a primenumber in my interval. Anyhow, I was just testing the speed so I stuck with it and started it up. First I sieved the range with NewPGen, then I used five other computers in parallell to reduce the lists, and finally checked any results that appeared with Proth. As I expected one prime I run that interval just to check the programs. Oooo, there was another number close to it, better try it out fast. The first prime checked out OK, the second too, but wait there was more... it was a factor of a Fermat number, F(91213). Finally I found something really nice! The same range produced four more gigantic primes, it was a really nice range I had selected! To celebrate the Fermat factor I have ordered a new computer to replace my old PII-233 at home. I've talked about it a lot but now I finally ordered an Athlon with a fast mainboard and memory. Is it here yet ? ... Is it here yet ? ... Is it here yet ? ... I'm waaaaaiiiting! :-) ... oh, it's here now and my 1.2GHz Athlon is 15% faster than the 1.5GHz P4 at work. Yeah! I like it! ... now running at 1.4GHz and with faster memories it beats the P4 by 35%! I REALLY like it! :-) Well, we came to the end my story, but it is by no means finished. I'll be back when I've found a Mersenne prime. ;-) 2002-03-06 Well, maybe not a Mersenne prime, but today I found my second Fermat factor. Yipeee! It was in a project to check all primes in the range k*2n+1 for k=800..20000, n=50000-59999. I started this search because I believed in it and I had the old P2-233 computer idle since I got my new one. It found the factor of F(50078) right in the beginning of the area at 7619*250081+1. Naturally I will now put all computers I could on this project. 2002-09-19 It's been half a year now and no more Fermat factors, only a few factors of generalised Fermat numbers. I've done more than half of the area now and the absence of interesting primes is quite frustrating. But I will prevail and do the full area before I give up hope. Until now I've found and tested over 3000 primes with 15000 digits.

Click here to see my current projects.

Here are some of the gigantic and rare primes I've found.

Special guest appearence : Nisse Blix's first gigantic prime :