Bill Allombert on Thu, 26 Jan 2012 12:01:30 +0100

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Re: questions

On Thu, Jan 26, 2012 at 01:42:22AM -0800, John W. Nicholson wrote:
> OK, I have some questions.
> Let us start with the following quote:
> "
> 3.13.26 primelimit: gp precomputes a list of all primes less than primelimit at initialization
> time. These are used by many arithmetic functions, usually for trial division purposes. If you do
> not plan to invoke any of them, you can just set this to 1. The maximal value is a little less than
> 2^32 (resp 2^64) on a 32-bit (resp. 64-bit) machine.
> Since almost all arithmetic functions eventually require some table of prime numbers, PARI
> currently guarantees that the rst 6547 primes, up to and including 65557, are precomputed, even
> if primelimit is 1.
> The default value is 500k.
> " 
> Q:
> What is the true value for "a little less 2^32 (resp 2^64) on a 32-bit (resp. 64-bit) machine"? 
> And, see what it did below?
> "
> ? primelimit=2^64
> %1 = 18446744073709551616

You should use default to change primelimit in GP:
? default(primelimit,2^64)

But in any case, it is not practically possible to go much higher than 10^10 due to
space/time constraint.