Contribution and Reservation

2·10²⁰²-1 =: 1(9)₂₀₂_<203>; = 7 · 97 · 193 · [152617000007630850000381542500019077125000953856250047692812502384640625119232031255961601562798080078139904003906995200195349760009767488000488374400024418720001220936000061046800003052340000152617_<198>] SUBMIT/RESERVE

Status

Expression:	2·10²⁰²-1
Composite Factor:	152617000007630850000381542500019077125000953856250047692812 502384640625119232031255961601562798080078139904003906995200 195349760009767488000488374400024418720001220936000061046800 003052340000152617 (198-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 202.90-digit and the GNFS difficulty is 197.18-digit. SNFS must be faster than GNFS. It will take about 24 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_202.
Put the following polynomial file 19999_202.poly in there too.
And then, run "perl factMsieve.pl 19999_202".

19999_202.poly ^*1

n: 152617000007630850000381542500019077125000953856250047692812502384640625119232031255961601562798080078139904003906995200195349760009767488000488374400024418720001220936000061046800003052340000152617
m: 20000000000000000000000000000000000000000
deg: 5
c5: 25
c0: -4
skew: 0.69
type: snfs
lss: 1
rlim: 16900000
alim: 16900000
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 198-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	118	Makoto Kamada	May 17, 2009
		1206	Andreas Tete	Jun 8, 2009
		1324 / 34
40	3e6	310	Andreas Tete	Jun 8, 2009
		310 / 1989
		/ 1679
45	11e6	0 / 4351 (487)
45	11e6	/ 4351 (487)
50	43e6	0 / 7534 (1241)
50	43e6	/ 7534 (1241)
55	11e7	0 / 17766 (3125)
55	11e7	/ 17766 (3125)

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

echo 152617000007630850000381542500019077125000953856250047692812502384640625119232031255961601562798080078139904003906995200195349760009767488000488374400024418720001220936000061046800003052340000152617 | ecm -n -c 1679 3e6

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

echo 152617000007630850000381542500019077125000953856250047692812502384640625119232031255961601562798080078139904003906995200195349760009767488000488374400024418720001220936000061046800003052340000152617 | ecm -n -c 4351 11e6

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

echo 152617000007630850000381542500019077125000953856250047692812502384640625119232031255961601562798080078139904003906995200195349760009767488000488374400024418720001220936000061046800003052340000152617 | ecm -n -c 7534 43e6

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

echo 152617000007630850000381542500019077125000953856250047692812502384640625119232031255961601562798080078139904003906995200195349760009767488000488374400024418720001220936000061046800003052340000152617 | ecm -n -c 17766 11e7

Submit factors

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