Observation for the day 27/2007

[Joerg Arndt]

Dear SeqFans,

With my friend fabien Sibenaler, we realized a Java program implementing the new
algorithm that gives the decomposition of a prime number (prime = weight * level
+ gap, or A000040(n) = A117078(n) * A117563(n) + A001223(n)).
This pgm is faster than the previous versions (Java and assembly said "naïfs").
This pgm Java load a MySQL table.
We look for the odd weights until sqrt (p) (zone 1) and if we did not find the
decomposition, we look for it by levels until (ln p)^2 (zone 2).
http://reismann.free.fr/classement.php
This limit is arbitrary and can be improved.
A minimum is imposed to avoid exceptions and if the following conjecture is
true, it should no more have exceptions :
conjecture : Except for p(6), p(11), p(30), p(32) and p(154), the weight of
prime numbers for which weight>level (zone 2) is prime.
The pgm assembler will soon be modified.
Java pgm :
http://reismann.free.fr/download/class_asm.zip
or on the "Download" page :
http://reismann.free.fr/telechargements.php

Two new pages will soon be created on my site. One on the algorithmie and the
other one on the conjectures based on my vision of prime numbers.

I thank Fabien for the development of pgm.

Best,

Rémi Eismann