Contribution and Reservation

2·10²²¹-1 =: 1(9)₂₂₁_<222>; = 691 · 1982518332226609_<16> · [145993908794679265280906834353269318371684848710417920434371722377619019393382275077652362615824360772720785594165434710205598804336757924268122265746121728432325491010807341661356795678826563563497827221_<204>] SUBMIT/RESERVE

Status

Expression:	2·10²²¹-1
Composite Factor:	145993908794679265280906834353269318371684848710417920434371 722377619019393382275077652362615824360772720785594165434710 205598804336757924268122265746121728432325491010807341661356 795678826563563497827221 (204-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 222.00-digit and the GNFS difficulty is 203.16-digit. SNFS must be faster than GNFS. It will take about 105 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 19999_221.
Put the following polynomial file 19999_221.poly in there too.
And then, run "perl factMsieve.pl 19999_221".

19999_221.poly ^*1

n: 145993908794679265280906834353269318371684848710417920434371722377619019393382275077652362615824360772720785594165434710205598804336757924268122265746121728432325491010807341661356795678826563563497827221
m: 10000000000000000000000000000000000000
deg: 6
c6: 1
c0: -5
skew: 1.31
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
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 204-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	0 / 0
35	1e6	118	Makoto Kamada	May 17, 2009
		118 / 904
		/ 786
40	3e6	0 / 2318 (280)
40	3e6	/ 2318 (280)
45	11e6	0 / 4475 (672)
45	11e6	/ 4475 (672)
50	43e6	0 / 7553 (1276)
50	43e6	/ 7553 (1276)

Command line to find prime factors up to about 35-digit

echo 145993908794679265280906834353269318371684848710417920434371722377619019393382275077652362615824360772720785594165434710205598804336757924268122265746121728432325491010807341661356795678826563563497827221 | ecm -n -c 786 1e6

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

echo 145993908794679265280906834353269318371684848710417920434371722377619019393382275077652362615824360772720785594165434710205598804336757924268122265746121728432325491010807341661356795678826563563497827221 | ecm -n -c 2318 3e6

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

echo 145993908794679265280906834353269318371684848710417920434371722377619019393382275077652362615824360772720785594165434710205598804336757924268122265746121728432325491010807341661356795678826563563497827221 | ecm -n -c 4475 11e6

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

echo 145993908794679265280906834353269318371684848710417920434371722377619019393382275077652362615824360772720785594165434710205598804336757924268122265746121728432325491010807341661356795678826563563497827221 | ecm -n -c 7553 43e6

Submit factors

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