Re: PrimeLimit

["cino hilliard" <hillcino368@hotmail.com>]

> From: Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>
> To: pari-users@list.cr.yp.to
> Subject: Re: PrimeLimit
> Date: Fri, 22 Sep 2006 14:40:44 +0200
>
> * Tautócrona [2006-09-20 15:20]:
> > I usually work with primes in Pari-GP, and find the PrimeLimit
> > parameter very small for my purposes. I know that with the command
> > Default(PrimeLimit, N) I can make PrimeLimit as big as N, but N ~
> > 4*10^9 seems to be the final limit.

> (11:22) gp > default(primelimit,2^31)
> time = 14,648 ms.
> (11:22) gp > gettime(); for (i=25,31, forprime(p=2,2^i,); print(gettime()))
> 60
> 124
> 228
> 444
> 845
> 1629
> 3140
>
> Nicely linear in forprime's upper bound...

The log of these is nicely linear.
1.77815125
2.093421685
2.357934847
2.64738297
2.926856709
3.211921084
3.496929648

You store the prime differences in the gp environment. Do you keep a running 
prime every so
often to increment from or do you just add up the differences?

I have beat the prime limit problem from the standpoint of prime(x) by using 
a sieve program to
store the  37,607,912,018 primes less than a trillion in binary format which 
requires 301 gigs of
file space. Then I call a prime  c program that reads this file with a 
prime2 routine in Pari.

prime2(n) =   \\ the nth prime using f:\sieve\primeapigcc.exe calling 
prime2-1000bill.bin
             {
             local(x,s);
             s=concat("f:/sieve/primeapigcc ",Str(n));
             s=concat(s," > temp.txt");   \\Must save to a temp file for 
correct output
             system(s);
             return(read("temp.txt"))
             }


For example.
(16:43:03) gp > prime2(37607912018)
%40 = 999999999989

The sieve program takes about 1/2 a day to store. I would like to use a 
difference scheme
to store many more primes in a lot less space. I guess the problem here will 
be speed again.

My guess that the ith prime for every million primes could be stored in a 
seperate file with a
value indication the record of the difference file. The we just add from 
that point.

This would reduce the file considerabley or allow a whole bunch more primes.

Enjoy,
Cino Hilliard,