2020-10-22, 13:46   #6
paulunderwood

Sep 2002
Database er0rr

3·11·107 Posts

Quote:
 Originally Posted by fivemack 10^10000 - 10^8668 - 1 is a pseudoprime; can I assert that it's prime because we've got a very boring factorisation of 86.68% of n+1 ?
Code:
./pfgw64 -tp -q"10^10000 - 10^8668 - 1" -T4
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000 - 10^8668 - 1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 43, base 1+sqrt(43)
10^10000 - 10^8668 - 1 is prime! (10.6651s+0.0255s)

Back in the day, we found this one when PRP tests took 100 mins each on Athlons at 1GHz.

What programs have you been using to find your prime?

The following was done on one core of a Haswell at 3.7GHz.

Code:
cat NRD_gigantic
ABC2 10^10000-10^\$a-1
a: from 1 to 9999
Code:
time ./pfgw64 -N -f NRD_gigantic
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Recognized ABC Sieve file:
ABC2 File

***WARNING! file NRD_gigantic may have already been fully processed.

10^10000-10^750-1 has factors: 2313617
10^10000-10^1589-1 has factors: 2635553
10^10000-10^3486-1 is 3-PRP! (1.1229s+0.0885s)
10^10000-10^3909-1 is 3-PRP! (1.0102s+0.1867s)
10^10000-10^4151-1 has factors: 376769
10^10000-10^5133-1 is 3-PRP! (1.0614s+0.0897s)
10^10000-10^5334-1 has factors: 772147
10^10000-10^6134-1 has factors: 2749921
10^10000-10^7928-1 is 3-PRP! (1.1574s+0.1369s)
10^10000-10^8072-1 has factors: 2742227
10^10000-10^8668-1 is 3-PRP! (0.9757s+0.0931s)
10^10000-10^8740-1 has factors: 2600837

real	34m58.010s
user	34m57.090s
sys	0m0.524s
Code:
./pfgw64 -tp -q"10^10000-10^3486-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^3486-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^3486-1 is prime! (3.8788s+0.0002s)

./pfgw64 -tp -q"10^10000-10^3909-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^3909-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^3909-1 is prime! (3.8218s+0.0001s)

./pfgw64 -tp -q"10^10000-10^5133-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^5133-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^5133-1 is prime! (3.9534s+0.0001s)

./pfgw64 -tp -q"10^10000-10^7928-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^7928-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^7928-1 is prime! (4.5040s+0.0002s)

Last fiddled with by paulunderwood on 2020-10-22 at 15:28