Karim Belabas on Sun, 25 May 2014 13:14:28 +0200

 Re: bug in PARI/GP (Segmentation Fault), please report.

```* John W. Nicholson [2014-05-25 12:55]:
[..]
> n=2;while(ln(prime(n))>ln(prime(n+1))/exp(1/(n))&&n<pl,n++);print(n)
>   ***   at top-level: ...=2;while(ln(prime(n))>ln(prime(n+1))/exp(1/(n
>   ***                                             ^--------------------
>   *** prime: bug in PARI/GP (Segmentation Fault), please report.
>   ***   Break loop: type 'break' to go back to GP prompt
> break> n
> 23163299
> break>
>
> Is this a bug on my machine, or can it be reproduced by others? Has this been reported before?

Can you try to narrow it down ?
With

n = 23163299
N = n + 1
alias(ln, log)

I can't reproduce it: the following command runs to completion

while(ln(prime(n))>ln(prime(n+1))/exp(1/(n))&&n<N,n++);
Cheers,

K.B.

P.S. Your program is inefficient: prime(n) runs in time O(n), so it runs
in time O~(N^2). Also (minor) prime(n+1) doesn't use the previously
computed prime(n). Much better:

test(N) =
{
n = 1; logprev = log(2);
forprime(p = 3, N,
my (l = log(p));   \\ l = log(prime(n+1)), logprev = log(prime(n))
if (logprev*exp(1/n) <  l, print([n, p]));
logprev = l; n++;
);
}

Untested but runs in time O~(N).

--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
`

```