Contribution and Reservation

(28·10²⁰³+53)/9 =: 3(1)₂₀₂7_<204>; = 47 · 193 · 23879 · [1436296887739416385925640414042924792272010340705621093192635454803699326879617449874768530561397705970514986521525829418607420388521888616467997080876360916500449029239532386648407578333063594213_<196>] SUBMIT/RESERVE

Status

Expression:	(28·10²⁰³+53)/9
Composite Factor:	143629688773941638592564041404292479227201034070562109319263 545480369932687961744987476853056139770597051498652152582941 860742038852188861646799708087636091650044902923953238664840 7578333063594213 (196-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 204.45-digit and the GNFS difficulty is 195.16-digit. SNFS must be faster than GNFS. It will take about 27 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 31117_203.
Put the following polynomial file 31117_203.poly in there too.
And then, run "perl factMsieve.pl 31117_203".

31117_203.poly ^*1

n: 1436296887739416385925640414042924792272010340705621093192635454803699326879617449874768530561397705970514986521525829418607420388521888616467997080876360916500449029239532386648407578333063594213
m: 20000000000000000000000000000000000000000
deg: 5
c5: 875
c0: 53
skew: 0.57
type: snfs
lss: 1
rlim: 17900000
alim: 17900000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

*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 196-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	0 / 0
40	3e6	265	Serge Batalov	Nov 9, 2008
		30	Serge Batalov	Nov 9, 2008
		295 / 2336
		/ 2041
45	11e6	0 / 4414 (592)
45	11e6	/ 4414 (592)
50	43e6	0 / 7542 (1258)
50	43e6	/ 7542 (1258)
55	11e7	0 / 17767 (3129)
55	11e7	/ 17767 (3129)

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

echo 1436296887739416385925640414042924792272010340705621093192635454803699326879617449874768530561397705970514986521525829418607420388521888616467997080876360916500449029239532386648407578333063594213 | ecm -n -c 2041 3e6

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

echo 1436296887739416385925640414042924792272010340705621093192635454803699326879617449874768530561397705970514986521525829418607420388521888616467997080876360916500449029239532386648407578333063594213 | ecm -n -c 4414 11e6

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

echo 1436296887739416385925640414042924792272010340705621093192635454803699326879617449874768530561397705970514986521525829418607420388521888616467997080876360916500449029239532386648407578333063594213 | ecm -n -c 7542 43e6

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

echo 1436296887739416385925640414042924792272010340705621093192635454803699326879617449874768530561397705970514986521525829418607420388521888616467997080876360916500449029239532386648407578333063594213 | ecm -n -c 17767 11e7

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