Contribution and Reservation

(32·10¹⁹⁵-41)/9 =: 3(5)₁₉₄1_<196>; = 653 · 170873 · [31865507768735611335350182975380267559751693248689024879125639862756811483559447839699360246457237408192995072942243435568726486049722334869281677497040762320693273236419629347563457372979_<188>] SUBMIT/RESERVE

Status

Expression:	(32·10¹⁹⁵-41)/9
Composite Factor:	318655077687356113353501829753802675597516932486890248791256 398627568114835594478396993602464572374081929950729422434355 687264860497223348692816774970407623206932732364196293475634 57372979 (188-digit)
Status:	Not factored. Not reserved. You can submit its factors or reserve it for submitting in the future.

How to factor it

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 196.51-digit and the GNFS difficulty is 187.50-digit. SNFS must be faster than GNFS. It will take about 15 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 35551_195.
Put the following polynomial file 35551_195.poly in there too.
And then, run "perl factMsieve.pl 35551_195".

35551_195.poly ^*1

n: 31865507768735611335350182975380267559751693248689024879125639862756811483559447839699360246457237408192995072942243435568726486049722334869281677497040762320693273236419629347563457372979
m: 2000000000000000000000000000000000000000
deg: 5
c5: 1
c0: -41
skew: 2.10
type: snfs
lss: 1
rlim: 13200000
alim: 13200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 188-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
30	25e4	430	Makoto Kamada	Nov 20, 2008
30	25e4	430 / 430
35	1e6	0 / 825
35	1e6	/ 825
40	3e6	0 / 2336 (294)
40	3e6	/ 2336 (294)
45	11e6	0 / 4479 (677)
45	11e6	/ 4479 (677)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

Command line to find prime factors up to about 35-digit

echo 31865507768735611335350182975380267559751693248689024879125639862756811483559447839699360246457237408192995072942243435568726486049722334869281677497040762320693273236419629347563457372979 | ecm -n -c 825 1e6

Command line to find prime factors up to about 40-digit

echo 31865507768735611335350182975380267559751693248689024879125639862756811483559447839699360246457237408192995072942243435568726486049722334869281677497040762320693273236419629347563457372979 | ecm -n -c 2336 3e6

Command line to find prime factors up to about 45-digit

echo 31865507768735611335350182975380267559751693248689024879125639862756811483559447839699360246457237408192995072942243435568726486049722334869281677497040762320693273236419629347563457372979 | ecm -n -c 4479 11e6

Command line to find prime factors up to about 50-digit

echo 31865507768735611335350182975380267559751693248689024879125639862756811483559447839699360246457237408192995072942243435568726486049722334869281677497040762320693273236419629347563457372979 | ecm -n -c 7553 43e6

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