Contribution and Reservation

(43·10²⁵⁰-7)/9 =: 4(7)₂₅₀_<251>; = 382055559643912628237678729323622320324517_<42> · [125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781_<210>] (Serge Batalov / GMP-ECM 6.2.1 B1=11000000, sigma=2259809016 for P42 / Jan 28, 2009) SUBMIT/RESERVE

Status

Expression:	(43·10²⁵⁰-7)/9
Composite Factor:	125054528253189447289899294516188810544311061053758161563935 547216828629946964499418093698568954568490304175173591891013 243054655738225373622583204023990174911869851275001232783069 648585566026456246963123490781 (210-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 253.63-digit and the GNFS difficulty is 209.10-digit. SNFS must be faster than GNFS. It will take about 1186 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 47777_250.
Put the following polynomial file 47777_250.poly in there too.
And then, run "perl factMsieve.pl 47777_250".

47777_250.poly ^*1

n: 125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781
m: 1000000000000000000000000000000000000000000
deg: 6
c6: 43
c0: -700
skew: 1.59
type: snfs
lss: 1
rlim: 118000000
alim: 118000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.8
alambda: 2.8

*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 210-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	Jan 27, 2009
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 125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781 | ecm -n -c 825 1e6

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

echo 125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781 | ecm -n -c 2336 3e6

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

echo 125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781 | ecm -n -c 4479 11e6

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

echo 125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781 | ecm -n -c 7553 43e6

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