Contribution and Reservation

(41·10¹⁹²-23)/9 =: 4(5)₁₉₁3_<193>; = 11593 · [392957436000651734284098641900763870918274437639571772238036362939321621284874972445057841417713754468692793543996856340511994786125727210864793889032653804498883425822095709096485427029721_<189>] SUBMIT/RESERVE

Status

Expression:	(41·10¹⁹²-23)/9
Composite Factor:	392957436000651734284098641900763870918274437639571772238036 362939321621284874972445057841417713754468692793543996856340 511994786125727210864793889032653804498883425822095709096485 427029721 (189-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 194.52-digit and the GNFS difficulty is 188.59-digit. SNFS must be faster than GNFS. It will take about 13 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 45553_192.
Put the following polynomial file 45553_192.poly in there too.
And then, run "perl factMsieve.pl 45553_192".

45553_192.poly ^*1

n: 392957436000651734284098641900763870918274437639571772238036362939321621284874972445057841417713754468692793543996856340511994786125727210864793889032653804498883425822095709096485427029721
m: 200000000000000000000000000000000000000
deg: 5
c5: 1025
c0: -184
skew: 0.71
type: snfs
lss: 1
rlim: 12200000
alim: 12200000
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 189-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-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
40	3e6	2336	Wataru Sakai	Aug 15, 2009
40	3e6	2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 392957436000651734284098641900763870918274437639571772238036362939321621284874972445057841417713754468692793543996856340511994786125727210864793889032653804498883425822095709096485427029721 | ecm -n -c 3962 11e6

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

echo 392957436000651734284098641900763870918274437639571772238036362939321621284874972445057841417713754468692793543996856340511994786125727210864793889032653804498883425822095709096485427029721 | ecm -n -c 7465 43e6

Command line to find prime factors up to about 55-digit

echo 392957436000651734284098641900763870918274437639571772238036362939321621284874972445057841417713754468692793543996856340511994786125727210864793889032653804498883425822095709096485427029721 | ecm -n -c 17751 11e7

Command line to find prime factors up to about 60-digit

echo 392957436000651734284098641900763870918274437639571772238036362939321621284874972445057841417713754468692793543996856340511994786125727210864793889032653804498883425822095709096485427029721 | ecm -n -c 42014 26e7

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