Re: [sage-devel] ERROR In function "is_prime"

[Vincent Delecroix]

Which version of sage are you using?

In a console I get

sage: k=ZZ(18878585599102049192211644417)
sage: k.is_prime()
True
sage: GF(k)
Finite Field of size 18878585599102049192211644417


Le 02/04/2022 à 02:30, carlos ortiz a écrit :
> The number:
>
> 18878585599102049192211644417 = 61*2^88+1
>
> but in sage:
>
> k=ZZ(18878585599102049192211644417)
>
> k.is_prime()
>
> True
>
> k.factor()
>
> 18878585599102049192211644417
>
> F = FiniteField(18)
>
> raise ValueError("the order of a finite field must be a prime power")
>
>
> Howeve,
>
> F=FiniteField(18878585599102049192211644417)
>
> F
>
> Finite Field of size 18878585599102049192211644417
>
> The above functions generate error for this number
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

[Andry Rabenantoandro]

It seems this number is a prime number and 18878585599102049192211644417 = 61*2^88+1 is not a factorization of the number. Hence, everything is fine. Am I missing something here?

cheers,

Andry

Le sam. 2 avr. 2022 à 02:33, carlos ortiz <pep...@gmail.com> a écrit :

The number:

18878585599102049192211644417 = 61*2^88+1

but in sage:

k=ZZ(18878585599102049192211644417)

k.is_prime()

True

k.factor()

18878585599102049192211644417

F = FiniteField(18)

raise ValueError("the order of a finite field must be a prime power")

Howeve, 

F=FiniteField(18878585599102049192211644417)

F

Finite Field of size 18878585599102049192211644417

The above functions generate error for this number

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Andry Nirina Rabenantoandro, PhD.

[Andrew]

There does seem to be a problem:

sage: k = 61*2^88+1 ; k
18878585599102049192211644417
sage: k.is_prime()
True
sage: k.factor()
18878585599102049192211644417
sage: k == 61*2^88+1
True
sage: GF(k)

Finite Field of size 18878585599102049192211644417

[John Cremona]

On Sat, 2 Apr 2022, 10:50 Andrew, <andrew...@gmail.com> wrote:

There does seem to be a problem:

sage: k = 61*2^88+1 ; k
18878585599102049192211644417
sage: k.is_prime()
True
sage: k.factor()
18878585599102049192211644417
sage: k == 61*2^88+1
True
sage: GF(k)
Finite Field of size 18878585599102049192211644417

What on earth is supposed to be the problem?  The only error message I have seen in this thread is in the original post where an attempt was made to construct GF(18).

To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/763afff3-3c26-4302-bd20-9d629ec04396n%40googlegroups.com.

[G. M.-S.]

Perhaps this is a hint?  The first message was sent on

Date: Fri, 1 Apr 2022 17:30:21 -0700 (PDT)

Guillermo