John Cremona wrote:
> It gets worse: (with GP/PARI 2.4.2):
>
> ? default(debug,2)
> %5 = 2
> ? p=nextprime(10^20)
> %6 = 100000000000000000039
> ? isprime(p)
> *** isprime: Warning: IFAC: untested integer declared prime.
> 507526619771207
> %7 = 1
>
> -- so one call to isprime(), which supposedly proves a proof, involves
> further calls (presumably) to fact() whose reults are not proved.
>
> Another email to pari-dev is in order...
>
I got this with SAGE (debug=4):
sage: p = next_prime(10^20)
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
*** Warning: Resetting all traps.
IFAC: cracking composite
507526619771207
IFAC: checking for pure square
OddPwrs: is 507526619771207
...a 3rd, 5th, or 7th power?
modulo: resid. (remaining possibilities)
211: 62 (3rd 0, 5th 0, 7th 0)
OddPwrs: examining 507526619771207
*** Warning: IFAC: untested integer declared prime.
IFAC: prime 507526619771207
appears with exponent = 1
IFAC: main loop: this was the last factor
IFAC: found 1 large prime (power) factor.
PL: proving primality of N = 100000000000000000039
PL: proving primality of N = 507526619771207
sage: p
100000000000000000039
I've seen this before. It is unclear to me why N = 507526619771207
is checked. In the end it seems primality is proved.
Jaap
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