## Re: request for comments on a prime generation algorithm

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• ... to ... to ... ********************************************************************** The following points might help. First, other than two & three all
Message 1 of 3 , Apr 17, 2002
> i am a newbie here and excuse my ignorance.this is to solicit the
> readers' opinion on the prime generation algorithm i struck
> upon.earlier i posted on this board that every prime other than 2 or
> 3
> is of the form sqrt(1+24*n).but the converse was not true and had
to
> use sieve for culling out the primes.for B steps the normal sieve
> generates B/log B primes in contrast to my approach which is
> k*sqrt(B).so i found another pattern which i am not sure if anybody
> else already did it.so here what i came up with for prime number
> generation of the first 1000 primes.This method also generates
> numbers
> like 25,35,49,etc which usually are product of primes generated
> earlier.
>
> i understand a lot can be optimised here and i am working on ways
to
> improve it.
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The following points might help. First, other than two & three all
prime numbers are congruent 5 Mod 6 or 1 Mod 6. Your equation of sprt
(1+24*n)is a correct represtation since it is a 1 Mod 6 number and
the square of a 5 Mod 6 number or a 1 Mod 6 number is a 1 Mod 6
number. The problem with you equation is that all it really achieves
is to show that every prime number squared plus 1 has a whole number
solution of n in your equation. There is no way to evaluate
primeness,if you will, when say a 1 Mod 6 number is not prime....it
will still have a solution in your equation [i.e. n=26... sqrt(1+24*
26=625)which is 25 squared]. Furthermore, let 5 Mod 6 numbers be
represented by 6X + 5 .... take this equation, square it and I think
you will start to see the "converse" of what you are trying to do.

Just some quick thoughts...perhaps others on this board can better