Re: bug?

["Karim Belabas" <Karim.Belabas@math.u-bordeaux1.fr>]

* Bill Allombert [2006-12-22 18:32]:
> On Fri, Dec 22, 2006 at 11:12:10AM -0600, Ariel Pacetti wrote:
>> I don't know whether this is a bug or it is made on purpose, but in gp, 
>> the following happens:
>> 
>> ? isprime(-3)
>> %1 = 0
> 
> PARI 2.1 return 1 so it is probably a bug.

Actually, when I wrote the isprime driver around Henri Cohen's APRCL
code and BPSW pseudoprimality test (both new in 2.3), I changed it on
purpose.

1) The docs say: "isprime(x): true (1) if x is a (proven) prime number".

[ In 2.1, we had "true if x is a strong pseudo-prime" ]

2) The most common definition for a prime number is "a positive integer
having exactly two divisors".

[ I don't think a function isprimeidealofZ() would be that useful.
  One would include 0, also. ]

On the other hand,

(11:47) gp > isprime(-2)
%1 = 0
(11:47) gp > isprime(-2,1)
%2 = 1
(11:47) gp > ispseudoprime(-2)
%3 = 1
(11:47) gp > ispseudoprime(-2,10)
%4 = 1

%2 should definitely be 0.

%4 follows precisely the old (partly broken: the number of compositeness tests
should depend on the input size) implementation.

Arguably, %2, %3 and %4 should also be changed to return 0, for consistency.

%%%%%%%%%%%%%%

Why do you need -3 to be reported as prime ?

    K.B.
-- 
Karim Belabas                  Tel: (+33) (0)5 40 00 26 17
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