A beautifull day, i have implemented the Sieve of Helmes and calculate it for x to 10^11. The sieve of Helmes is another prime generator, which has nothing to do with the sieve of Eratosthenes. It bases on quadratic polynoms and the periodic occurence of the primes in the polynom.
I found 70.000.000.000 Primes, some of them bigger than 2^64 Is there a real chance to find factors of Mersenne numbers ? I would like to calculate the primes on these polynom up to 10^12 or higher, but my algorithm needs for that approximately 1 Terabyte of disk space, but approximately only 12 days of runtime to calculate the primes. I tried to check some Mersenne Numbers, where no factors are found, but i did not succeed. You can find all Mersenne Numbers on the polynom f(x)=2x^2-1 since you can write 2^p-1 = 2*2^[(p-1)/2] -1 f(2)=7, f(4)=17, f(8)=127 and so on (f(2^((p-1)/2))=2^p-1 Therefore all factors of Mersenne Numbers can be found on these special polynom. Beside you find all primes mod 8 = 1 or 7 on these polynom, but not in an order. The primes mod 8 = 3 or 5 could not be a factor of Mersenne Numbers. Therefore half of the primes could be eleminated for the search. I needed approximately 30h on an Athlon (4000) with 4GB Ram and 100MB disk space for calculating 10^11. A basic Implementation can be found under http://www.devalco.de/quadr_Sieb_2x%5E2-1.htm Best regards from the primes Bernhard Helmes -- www.devalco.de Development of Algorithmic Constructions www.rabbitweb.de Jugglevideos www.beablue.de personal web page Tel.: 0241 / 99 77 55 22 in Germany (0049) Psssst! Schon das coole Video vom GMX MultiMessenger gesehen? Der Eine für Alle: http://www.gmx.net/de/go/messenger03 _______________________________________________ Prime mailing list Prime@hogranch.com http://hogranch.com/mailman/listinfo/prime
