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Old 2004-04-27, 16:06   #8
geoff
 
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Mar 2003
New Zealand

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It is possible to do stage one P-1 on 2^2N-1 with Prime95 then continue with stage two on 2^N-1 or 2^N+1 separately with gmp-ecm by using the splitcf program (see http://www.mersenneforum.org/showpos...7&postcount=13). Here is a (trivial) example of doing P-1 on 2^893+1 using this method (some output snipped):

$
$ cat worktodo.ini
Pminus1=1786,3000,1,0,0
$
$ cat lowm.txt
M( 1786 )C: 3
M( 1786 )C: 283
M( 1786 )C: 1787
M( 1786 )C: 174763
M( 1786 )C: 2351
M( 1786 )C: 4513
M( 1786 )C: 524287
M( 1786 )C: 13264529
M( 1786 )C: 6705767506519
$
$ mprime -d
Mersenne number primality test program version 23.5
P-1 on M1786 with B1=3000, B2=3000
M1786 stage 1 complete. 8682 transforms. Time: 0.032 sec.
Stage 1 GCD complete. Time: 0.002 sec.
$
$ pm1dump m0001786 | splitcf -p | ecm -resume - 3000 16000
GMP-ECM 5.0.3 [powered by GMP 4.1.2] [ECM]
Resuming P-1 residue
Input number is 249060...665097 (258 digits)
Using B1=3000-3000, B2=16000, polynomial Dickson(4)
Step 1 took 0ms
Step 2 took 33ms
********** Factor found in step 2: 165768537521
Found probable prime factor of 12 digits: 165768537521
Composite cofactor 150245...858457 has 247 digits

This might be useful for doing P-1 of the Fermat numbers, stage one could be done just once on F(N)-2 with mprime, then using the same save file in each case, do stage two with gmp-ecm on F(N-1), F(N-2), F(N-3), etc.

E.g. if stage one has been done on 2^262144-1 to B1 and the save file is called m0262144, then run these commands (with appropriate low[mp].txt in the current directory) to do stage two on 2^131072+1, 2^65536+1, and 2^32768+1.

pm1dump m0262144 | splitcf -p | ecm -resume - B1 B2
pm1dump m0262144 | splitcf -m | splitcf -p | ecm -resume - B1 B2
pm1dump m0262144 | splitcf -m | splitcf -m | splitcf -p | ecm -resume - B1 B2
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