cino hilliard on Sun, 08 Jan 2006 02:05:08 +0100


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RE:>Subject: RE: Need Help!!!!!!!! ;-) 

Hi Raúl,


From: "cino hilliard" <hillcino368@hotmail.com>
Subject: RE: Need Help!!!!!!!! ;-)
Date: Fri, 30 Dec 2005 20:43:31 +0000
Hi,

Hi!
I try to make a program to compute primes between 2^508 and 2^512.
This is pretty much an impossibility when you subtract Riemann's estimates of Pi(x), 
R(x) =     \\ Riemann's approx of Pi(x)
     {
     local(j);
      round(sum(j=1,200,moebius(j)*Li(x^(1/j))/j))
     }


(14:24) gp > R(2^512) - R(2^508)
%4 = 355004533527221885776819035743684578740476405756751288608929750922829224386 
33238391150416079096446554062311754342976116352879437331560723871759964007562
This is am approximation of the number of primes between  2^508 and 2^512.
So if your program could just check primes it would have to check 10^151 of then, a formidable 
task indeed.

For shorter bounds you may want to try

c=0;forstep(x=2^508+1,2^508+1000,2,if(ispseudoprime(x),c++;print1(x",")))
"These big primes sat on a wall. These big primes had a great fal.l And all the Kings computers and all the Kings programmers couldn't put these primes back together again." 

Cino