Contribution and Reservation

10²⁴¹+3 =: 1(0)₂₄₀3_<242>; = 13 · 263 · 11339641 · 220989484351_<12> · 16360448922352966372489253141_<29> · [71340273312409237591261917243869527077291161550601511002282830918989575724135262596617428035963174528565690329235010543929957349891462128903258187994400811641741461562217217830313310266909827_<191>] (Wojciech Florek) SUBMIT/RESERVE

Status

Expression:	10²⁴¹+3
Composite Factor:	713402733124092375912619172438695270772911615506015110022828 309189895757241352625966174280359631745285656903292350105439 299573498914621289032581879944008116417414615622172178303133 10266909827 (191-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 241.00-digit and the GNFS difficulty is 190.85-digit. SNFS must be faster than GNFS. It will take about 450 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 10003_241.
Put the following polynomial file 10003_241.poly in there too.
And then, run "perl factMsieve.pl 10003_241".

10003_241.poly ^*1

n: 71340273312409237591261917243869527077291161550601511002282830918989575724135262596617428035963174528565690329235010543929957349891462128903258187994400811641741461562217217830313310266909827
m: 10000000000000000000000000000000000000000
deg: 6
c6: 10
c0: 3
skew: 0.82
type: snfs
lss: 1
rlim: 73000000
alim: 73000000
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 191-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	Dec 15, 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 71340273312409237591261917243869527077291161550601511002282830918989575724135262596617428035963174528565690329235010543929957349891462128903258187994400811641741461562217217830313310266909827 | ecm -n -c 825 1e6

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

echo 71340273312409237591261917243869527077291161550601511002282830918989575724135262596617428035963174528565690329235010543929957349891462128903258187994400811641741461562217217830313310266909827 | ecm -n -c 2336 3e6

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

echo 71340273312409237591261917243869527077291161550601511002282830918989575724135262596617428035963174528565690329235010543929957349891462128903258187994400811641741461562217217830313310266909827 | ecm -n -c 4479 11e6

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

echo 71340273312409237591261917243869527077291161550601511002282830918989575724135262596617428035963174528565690329235010543929957349891462128903258187994400811641741461562217217830313310266909827 | ecm -n -c 7553 43e6

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