help with Pari

[r.shepherd]

Don Reble wrote (in part):

>     Is the number "25 1097226443 0988869706 6444184023 1990201201
>     8513329120 2368754457 4398706423" prime, or not?
>     (It's the 81st cyclotomic polynomial, evaluated at 21.)
>

Primo (1.2.1, unregistered version) also says prime.  If you'd like to see
the Primo certificate, send me an e-mail and I'll send it to you.  Primo
required only 10 tests (EC, N-1, N+1, and finally SPP tests).

>     And if I ask Pari-2.2.5 to do that,
>         isprime(..., 1)
>     it generates the same certificate.
>
>     But if I ask Pari-2.2.5 to use APRCL,
>         isprime(..., 2)
>     it says, "composite". What does your Pari say?
>

Just for the record, the version of Pari I have been using is old, version
2.0.17 (beta).  It does not permit a second argument with isprime, hence
only supports the probabilistic prime tests (strong pseudoprime to up to
10 randomly chosen bases).  Yes, isprime() returns 1.  (If I remember
correctly, it's possible to set a debug flag so as to observe which bases
are chosen -- and multiple calls to isprime with the same number will
pick different bases.  I just don't remember how to set that debug flag
off the top of my head.  If you want to know more about these debug
flags, say that in your e-mail, too, and I'll dig that up.).

Rick

> --
> Don Reble       djr at nk.ca