Contribution and Reservation

4·10²⁴³+1 =: 4(0)₂₄₂1_<244>; = 167 · 499 · 33461534459_<11> · 38246818028611_<14> · [37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853_<215>] SUBMIT/RESERVE

Status

Expression:	4·10²⁴³+1
Composite Factor:	375060918032323002461539640377513600520701992873440097014301 440950058439086924757932398522055487853383366701347332340233 243418721779091707240550336637172977510215666085379853270246 06478204000425747591569480230901853 (215-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 243.90-digit and the GNFS difficulty is 214.57-digit. SNFS must be faster than GNFS. It will take about 562 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 40001_243.
Put the following polynomial file 40001_243.poly in there too.
And then, run "perl factMsieve.pl 40001_243".

40001_243.poly ^*1

n: 37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853
m: 20000000000000000000000000000000000000000
deg: 6
c6: 125
c0: 2
skew: 0.50
type: snfs
lss: 1
rlim: 81000000
alim: 81000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
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 215-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	825	Wataru Sakai	Feb 21, 2009
35	1e6	825 / 825
40	3e6	0 / 2111
40	3e6	/ 2111
45	11e6	0 / 4441 (612)
45	11e6	/ 4441 (612)
50	43e6	0 / 7548 (1266)
50	43e6	/ 7548 (1266)
55	11e7	0 / 17769 (3131)
55	11e7	/ 17769 (3131)

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

echo 37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853 | ecm -n -c 2111 3e6

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

echo 37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853 | ecm -n -c 4441 11e6

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

echo 37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853 | ecm -n -c 7548 43e6

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

echo 37506091803232300246153964037751360052070199287344009701430144095005843908692475793239852205548785338336670134733234023324341872177909170724055033663717297751021566608537985327024606478204000425747591569480230901853 | ecm -n -c 17769 11e7

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