Output of "example Atkin;" from "atkins.lib";
Code:
>example Atkin;
// proc Atkin from lib atkins.lib
EXAMPLE:
ring R = 0,x,dp;
Atkin(7691,100,5);
-1
Atkin(3473,10,2);
-1
printlevel=1;
Atkin(10000079,100,2);
Set i = 0, n = 0 and N(i) = N(0)= 10000079.
pause>
List H of possibly suitable discriminants will be calculated.
H = -3,-4,-7,-8,-11,-12,-15,-16,-19,-20,-23,-24,-27,-28,-31,-32,-35,-36,-39,-40,-43,-44,-47,-48,-51,-52,-55,-56,-59,-60,-63,-64,-67,-68,-71,-72,-75,-76,-79,-80,-83,-84,-87,-88,-91,-92,-95,-96,-99,-100,-103,-104,-107,-108,-111,-112,-115,-116,-119,-120,-123,-124,-127,-128,-131,-132,-135,-136,-139,-140,-143,-144,-147,-148,-151,-152,-155,-156,-159,-160,-163,-164,-167,-168,-171,-172,-175,-176,-179,-180,-183,-184,-187,-188,-191,-192,-195,-196,-199,-200
pause>
N(0) = 10000079 is divisible by 5.
pause>
N(0) = N = 10000079 and therefore N is not prime.
pause>
-1
>
// proc Atkin from lib atkins.lib
EXAMPLE:
ring R = 0,x,dp;
Atkin(7691,100,5);
-1
Atkin(3473,10,2);
-1
printlevel=1;
Atkin(10000079,100,2);
Set i = 0, n = 0 and N(i) = N(0)= 10000079.
pause>
List H of possibly suitable discriminants will be calculated.
H = -3,-4,-7,-8,-11,-12,-15,-16,-19,-20,-23,-24,-27,-28,-31,-32,-35,-36,-39,-40,-43,-44,-47,-48,-51,-52,-55,-56,-59,-60,-63,-64,-67,-68,-71,-72,-75,-76,-79,-80,-83,-84,-87,-88,-91,-92,-95,-96,-99,-100,-103,-104,-107,-108,-111,-112,-115,-116,-119,-120,-123,-124,-127,-128,-131,-132,-135,-136,-139,-140,-143,-144,-147,-148,-151,-152,-155,-156,-159,-160,-163,-164,-167,-168,-171,-172,-175,-176,-179,-180,-183,-184,-187,-188,-191,-192,-195,-196,-199,-200
pause>
N(0) = 10000079 is divisible by 5.
pause>
N(0) = N = 10000079 and therefore N is not prime.
pause>
-1
>
In particular 10000079 should be a prime number, the message "10000079 is divisible by 5" is noncence.
The reason for the problem is the usage of "a mod b" with number type.
Code:
> ring r =0, x, dp;
> 10000079 mod 5;
4
> number(10000079) mod 5;
0
>
> 10000079 mod 5;
4
> number(10000079) mod 5;
0
>
I suppose the problem with the library exists since years.
