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Bill Allombert on Mon, 08 Jul 2024 14:51:33 +0200
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Re: Are there known false positives for GP ispseudoprime() ?
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: Are there known false positives for GP ispseudoprime() ?
- From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Date: Mon, 8 Jul 2024 14:46:29 +0200
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On Mon, Jul 08, 2024 at 01:11:32PM +0200, hermann@stamm-wilbrandt.de wrote:
> Are there known non-prime numbers where GP ispseudoprime returns 1
> without passing flag?
No. The doc says:
There are no known composite numbers passing the above test, although it is expected that infinitely many such numbers exist. In
particular, all composites <= 2^{64} are correctly detected (checked using
http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html).
> Or with other flag values?
Yes, but they depend on the random seed;
? for(N=1,oo,setrand(1);if(ispseudoprime(N,1)&&!isprime(N),return(N)))
%22 = 51
? for(N=1,oo,setrand(1);if(ispseudoprime(N,2)&&!isprime(N),return(N)))
%23 = 949
? for(N=1,oo,setrand(1);if(ispseudoprime(N,3)&&!isprime(N),return(N)))
%24 = 22028203
Cheers,
Bill.