Re^2: Math help: Finding Prime Numbers

Math::Pari is great--I wish I understood more of it than the ~1% that currently I do :)--but it's not so good for primes. By default (AS PPM version), primes() only knows the first 41561 primes:

C:\test>p1
Perl> use Math::Pari qw[ prime primes nextprime precprime ];;

Perl> print prime 41561;;
500257

Perl> print prime 41562;;
PARI:   *** not enough precalculated primes at (eval 7) line 1, <STDIN
+> line 4.
[download]

It will generate larger primes using nextprime(), but it pretty slow, taking around 64 seconds to get to the 1 millionth:

Perl> 
print scalar localtime; 
$p = 500257; 
$p = nextprime ++$p for 41562 .. 1000000; 
print scalar localtime; 
print $p;;

Tue Nov 14 04:36:02 2006
Tue Nov 14 04:37:07 2006
15485863
[download]

But the biggest problem is that it forgets all the bigger primes as soon as it has returned them (below is a continuation of the previous session):

Perl> print prime 41562;;
PARI:   *** not enough precalculated primes at (eval 9) line 1, <STDIN
+> line 6.
[download]

From the error message I guess it might be possible to increase the number of precalculated primes if you manage to build it yourself? But if you Linux guys have trouble with it, you can guess my chances :)

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Re^3: Math help: Finding Prime Numbers by Zaxo (Archbishop) on Nov 14, 2006 at 05:21 UTC
The `$Math::Pari::initprimes` variable controls initialization of precalculated primes. Since that doesn't go through the perl iface, but is a canned C routine, initialization is fast. To avoid setting that in a `BEGIN` block, you can say: `use Math::PariInit qw( primes=12000000 );` [download] See the Initialization section of the Math::Pari docs. After Compline, Zaxo	[reply] [d/l]