Contribution and Reservation

(25·10²²⁵-1)/3 =: 8(3)₂₂₅_<226>; = 13 · 67 · 22093 · 82781773 · [5231318746814481185333349904310041380229822631797259235645029384678455540250981418483754261996601856404675654784579415224115627516844982371597912049684871938972755096362639060883092454522755193347735232639524907_<211>] SUBMIT/RESERVE

Status

Expression:	(25·10²²⁵-1)/3
Composite Factor:	523131874681448118533334990431004138022982263179725923564502 938467845554025098141848375426199660185640467565478457941522 411562751684498237159791204968487193897275509636263906088309 2454522755193347735232639524907 (211-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 227.10-digit and the GNFS difficulty is 210.72-digit. SNFS must be faster than GNFS. It will take about 155 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 83333_225.
Put the following polynomial file 83333_225.poly in there too.
And then, run "perl factMsieve.pl 83333_225".

83333_225.poly ^*1

n: 5231318746814481185333349904310041380229822631797259235645029384678455540250981418483754261996601856404675654784579415224115627516844982371597912049684871938972755096362639060883092454522755193347735232639524907
m: 50000000000000000000000000000000000000
deg: 6
c6: 8
c0: -5
skew: 0.92
type: snfs
lss: 1
rlim: 43000000
alim: 43000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
rlambda: 2.7
alambda: 2.7

*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 211-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	Oct 22, 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 5231318746814481185333349904310041380229822631797259235645029384678455540250981418483754261996601856404675654784579415224115627516844982371597912049684871938972755096362639060883092454522755193347735232639524907 | ecm -n -c 825 1e6

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

echo 5231318746814481185333349904310041380229822631797259235645029384678455540250981418483754261996601856404675654784579415224115627516844982371597912049684871938972755096362639060883092454522755193347735232639524907 | ecm -n -c 2336 3e6

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

echo 5231318746814481185333349904310041380229822631797259235645029384678455540250981418483754261996601856404675654784579415224115627516844982371597912049684871938972755096362639060883092454522755193347735232639524907 | ecm -n -c 4479 11e6

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

echo 5231318746814481185333349904310041380229822631797259235645029384678455540250981418483754261996601856404675654784579415224115627516844982371597912049684871938972755096362639060883092454522755193347735232639524907 | ecm -n -c 7553 43e6

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