A beautifull day, This is only a suggestion for sieving Mersenne Primes with a prime sieve.
All Mersenne numbers occurs on the quadratic polynom 2x²-1. Proof: 2^p-1 = 2 ^(2m+1) - 1 = 2*2^(2m) -1 = 2*2^m*2^m -1 = 2 *(2^m)² - 1 You can sieve on these quadratic polynom with the following algorithm http://www.devalco.de/quadr_Sieb_2x%5E2-1.htm Accordingly only the primes mod 8 = 1 or mod 8 = 7 can be factors of Mersennen numbers There is a relationship between sieving on the polynom f(x)=2x²-1 and the Mersenne numbers. The Mersenne numbers occurs as a potence of 2. For example f(2)=7, f(4)=31, f(8)=127, f(64)=8191 and so on. I am not sure if the sieving on the polynom 2x² -1 is for practical sense. But the theorical background might be interesting for you. Nice Greetings 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) GMX startet ShortView.de. Hier findest Du Leute mit Deinen Interessen! Jetzt dabei sein: http://www.shortview.de/[EMAIL PROTECTED] _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
