Mentions légales du service

Skip to content

Add reducefactors to find primes from many composites in stage1 GPU code

Seth Troisi requested to merge step1_multiple_factors_final into master

Try to determine the prime factors from an overlapping set of composite factors

(these are heavily edited for brevity)

Before

echo "101^2*1013*1000003*1000033*1000037*1000039*1000081^2*(2^89-1)^2" | ./ecm -gpu -gpucurves 1024 -sigma 3:1000 10000
Using B1=10000, B2=1873422, sigma=3:1000-3:2023 (1024 curves)
GPU: factor 10335659184464100091253526654407 found in Step 1 with curve 0 (-sigma 3:1000)
GPU: factor 10334016010907 found in Step 1 with curve 1 (-sigma 3:1001)
GPU: factor 10335700525736575955950356673123 found in Step 1 with curve 2 (-sigma 3:1002)
GPU: factor 10336072609839250164662144750599 found in Step 1 with curve 3 (-sigma 3:1003)
...
Computing 1024 Step 1 took 51ms of CPU time / 1691ms of GPU time
********** Factor found in step 1: 10335721196372813888298771682481
********** Factor found in step 1: 1000033
********** Factor found in step 1: 1000037
Found prime factor of 7 digits: 1000037
Composite cofactor (((101^2*1013*1000003*1000033*1000037*1000039*1000081^2*(2^89-1)^2)/10335721196372813888298771682481)/1000033)/1000037 has 54 digits

After

$ echo "101^2*1013*1000003*1000033*1000037*1000039*1000081^2*(2^89-1)^2" | ./ecm -gpu -gpucurves 1024 -sigma 3:1000 10000
Using B1=10000, B2=1873422, sigma=3:1000-3:2023 (1024 curves)
GPU: factor 10335659184464100091253526654407 found in Step 1 with curve 0 (-sigma 3:1000)
GPU: factor 10334016010907 found in Step 1 with curve 1 (-sigma 3:1001)
GPU: factor 10335700525736575955950356673123 found in Step 1 with curve 2 (-sigma 3:1002)
...
GPU: factor 10334367368536438055024419 found in Step 1 with curve 1021 (-sigma 3:2021)
GPU: factor 10335659184464100091253526654407 found in Step 1 with curve 1022 (-sigma 3:2022)
GPU: factor 10335721196372813888298771682481 found in Step 1 with curve 1023 (-sigma 3:2023)
Computing 1024 Step 1 took 31ms of CPU time / 1744ms of GPU time
********** Factor found in step 1: 1000003
********** Factor found in step 1: 1000033
********** Factor found in step 1: 1000037
********** Factor found in step 1: 1000039
********** Factor found in step 1: 10333613
********** Factor found in step 1: 1000162006561
Composite cofactor ((((((101^2*1013*1000003*1000033*1000037*1000039*1000081^2*(2^89-1)^2)/1000003)/1000033)/1000037)/1000039)/10333613)/1000162006561 has 54 digits

Note that 101^2*1013 appears in all found factors so it appears as a composite factor found (10333613) the same with 1000081^2 appearing as 1000162006561

Merge request reports