Re: efficient determination of smallest quadratic non-residue / t++ works, t=nextprime(t) hangs

[hermann@stamm-wilbrandt.de]

On 2023-06-09 13:04, Bill Allombert wrote:
> On Fri, Jun 09, 2023 at 11:26:25AM +0200, hermann@stamm-wilbrandt.de 
> wrote:
> ...
> But it is much better to use forprime
> forprime(t=2,oo,if( kronecker(t, m)==-1, return(t)));
> or
> forprime(tt=2,oo,if( kronecker(tt, m)==-1, t=tt; break()));
>
> > 2)
> > Is there a better way (like C/C++/Python argv) than I did to pass 
> > value of
> > "n" when executing a script with "gp .... < script.gp"?
>
> Not really, but you can use environment variables.
> env GPARG1="3756801695685 * 2 ^ 666669 + 1" gp < script.gp
> and in your script do
> n = eval(Strexpand("$GPARG1"));
> to get n.
Thanks, I took the first forprime() loop.

But eval(Strexpand("$GPARG1")) resulted in warning in case environment 
variable is not set.
Nevertheless environment variable looks much nicer, so I used "getenv()" 
instead:
https://github.com/Hermann-SW/RSA_numbers_factored/blob/main/pari/smallest_qnr.gp


pi@pi400-64:~ $ n="3756801695685 * 2 ^ 666669 + 1"  gp -q < 
smallest_qnr.gp
n is 200700-digit number
  ***   last result: cpu time 1 ms, real time 1 ms.
smallest quadratic non-residue of n: 31
pi@pi400-64:~ $
pi@pi400-64:~ $ gp -q < smallest_qnr.gp
Format: n="value"  gp -q < smallest_qnr.gp
10000/36401/100355/200700/272770/330855/388342-digit number examples:
n="(10 ^ 10000 - 1) \ 3 - 10 ^ 6333"
n="34*((10^36400-1)\9)-42000040044444004000024*10^2264*((10^36400-1)\9)\((10^4550-1)\9)-1"
n="65516468355 * 2 ^ 333333 + 1"
n="3756801695685 * 2 ^ 666669 + 1"
n="1705 * 2 ^ 906110 + 1"
n="2145 * 2 ^ 1099064 + 1"
n="2996863034895 * 2 ^ 1290000 + 1"
pi@pi400-64:~ $



Regards,

Hermann Stamm-Wilbrandt.