cino hilliard on Sun, 24 Sep 2006 15:01:11 +0200 |
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Re: PrimeLimit |
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 3.496929648You 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 = 999999999989The 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,