Re: Is short-circuit evaluation possible with parfor() ?

[hermann@stamm-wilbrandt.de]

On 2026-02-10 10:26, Ruud H.G. van Tol wrote:
> Hello Hermann,
>
> I expect it to be related to your nbthreads setting.
>
> Mine is at 10. I hardly ever go over 12, to avoid overhead.
That is the reason why nbthreads is 16 on my 16C/32T AMD 7950X system.
And why nbthreads is 192 on my 192C/384T 8-socket server.
One gp thread per really existing core.


> I don't call export(), as I think that for this case it is superfluous.
I was forced to use that by GP, but now learned that your "my(...)" is 
OK as well.


return() works as documented, but 1994 was a bad input to measure.
1995 is good, because the 445th prime tested aborts.


So my first script without early abort takes 32 seconds real time:

hermann@x3950-X6:~$ gp
...
                 GP/PARI CALCULATOR Version 2.17.3 (released)
...
                  threading engine: pthread, nbthreads = 192
...
? isok2(n) = 
{s=0;p=prime(n+1)#;export(s,p);parfor(i=2,n+1,ispseudoprime(1+p/prime(i)),r,s+=r);s==0};
? #
   timer = 1 (on)
? isok2(1995)
cpu time = 1h, 37min, 20,393 ms, real time = 31,751 ms.
%2 = 0
?


Now with return real time gets reduced to 17 seconds (and CPU time down 
to 50min from 1:37h)!

? isok3(n) = 
{my(p=prime(n+1)#);parfor(i=2,n+1,ispseudoprime(1+p/prime(i)),r,if(r,return(0)););1};
? isok3(1995)
cpu time = 50min, 22,570 ms, real time = 17,110 ms.
%4 = 0
?


Btw, GP ispseudoprime() is good for a few 1000 decimal digit 
computations:

? #digits(1995#)
836
?


For bigger numbers I let GP do the parallel orchestration and let it 
call out to pfgw64 that is based on gwnum lib that does big number 
computations superfast (on Intel/AMD CPUs only). For numbers with less 
than 800,000 decimal digits gwnum does not use multithreading, and so 
running 192× pfgw64 in paralel is good on the 8-socket server.


For n=20489 I started "nohup ./doitpar" with this script:

hermann@x3950-X6:~/pfgw/distribution$ cat doitpar
#!/bin/bash
time numactl -C 0-191 gp -q < relaxed.par.gp
hermann@x3950-X6:~/pfgw/distribution$


With this GP script:

hermann@x3950-X6:~/pfgw/distribution$ cat relaxed.par.gp
n=20489;export(n);

parfor(i=2,n+1,if(0==system("./pfgw64 -tm 
-q\""prime(n+1)"#/"prime(i)"+1\" -Cquiet 2>/dev/null 
>/dev/null"),print("\nfound: "i"\n");return(0),print(i);system("date");));
hermann@x3950-X6:~/pfgw/distribution$



The whole computation completed in 5:44h real time (45.6d cpu time):

hermann@x3950-X6:~/pfgw/distribution$ tail -5 nohup.out.343m
Sat Feb  7 11:56:15 PM CET 2026

real	343m16.938s
user	65710m17.430s
sys	50m52.422s
hermann@x3950-X6:~/pfgw/distribution$


20489 does not belong to A391020 because three primes p with 
(20489+1)#/p+1 were found:

hermann@x3950-X6:~/pfgw/distribution$ grep found nohup.out.343m
found: 3765
found: 12120
found: 13351
hermann@x3950-X6:~/pfgw/distribution$


Those are the indices reported, for the lowest here is pfgw64 prime 
proof — the first prime with 100K decimal digits I found and proved 
prime:

? prime(20489+1)
230597
? prime(3765)
35339
? #digits(prime(20489+1)#/prime(3765))
100010
?

hermann@7950x:~/pfgw/distribution$ time ./pfgw64 -tm -q"230597#/35339+1"
PFGW Version 4.1.3.64BIT.20240114.x86_Dev [GWNUM 30.19]

Primality testing 230597#/35339+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 33.33%
230597#/35339+1 is prime! (289.7452s+0.0279s)


real    4m49,793s
user    4m50,125s
sys    0m0,055s
hermann@7950x:~/pfgw/distribution$


Proving BIG numbers prime can earn you 150,000 USD price money ;-)

https://www.eff.org/awards/coop


Regards,

Hermann.