Contribution and Reservation

(73·10²⁰⁴-1)/9 =: 8(1)₂₀₄_<205>; = 23 · 46521463 · [7580522668234184174219440727831003332535772005419736011078988293239029413258798801628317993045499946804928288981938724676590216949139210368445010378852361871459211914547645236641129924231084021239_<196>] SUBMIT/RESERVE

Status

Expression:	(73·10²⁰⁴-1)/9
Composite Factor:	758052266823418417421944072783100333253577200541973601107898 829323902941325879880162831799304549994680492828898193872467 659021694913921036844501037885236187145921191454764523664112 9924231084021239 (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 206.86-digit and the GNFS difficulty is 195.88-digit. SNFS must be faster than GNFS. It will take about 33 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 81111_204.
Put the following polynomial file 81111_204.poly in there too.
And then, run "perl factMsieve.pl 81111_204".

81111_204.poly ^*1

n: 7580522668234184174219440727831003332535772005419736011078988293239029413258798801628317993045499946804928288981938724676590216949139210368445010378852361871459211914547645236641129924231084021239
m: 100000000000000000000000000000000000000000
deg: 5
c5: 73
c0: -10
skew: 0.67
type: snfs
lss: 1
rlim: 19600000
alim: 19600000
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	118	Makoto Kamada	May 26, 2009
		326	Dmitry Domanov	Jun 2, 2009
		444 / 0
40	3e6	426	Dmitry Domanov	Jun 2, 2009
		426 / 1273
		/ 847
45	11e6	277	Dmitry Domanov	Jun 2, 2009
		277 / 4366 (523)
		/ 4089 (246)
50	43e6	0 / 7473 (1166)
50	43e6	/ 7473 (1166)
55	11e7	0 / 17748 (3100)
55	11e7	/ 17748 (3100)

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

echo 7580522668234184174219440727831003332535772005419736011078988293239029413258798801628317993045499946804928288981938724676590216949139210368445010378852361871459211914547645236641129924231084021239 | ecm -n -c 847 3e6

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

echo 7580522668234184174219440727831003332535772005419736011078988293239029413258798801628317993045499946804928288981938724676590216949139210368445010378852361871459211914547645236641129924231084021239 | ecm -n -c 4089 11e6

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

echo 7580522668234184174219440727831003332535772005419736011078988293239029413258798801628317993045499946804928288981938724676590216949139210368445010378852361871459211914547645236641129924231084021239 | ecm -n -c 7473 43e6

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

echo 7580522668234184174219440727831003332535772005419736011078988293239029413258798801628317993045499946804928288981938724676590216949139210368445010378852361871459211914547645236641129924231084021239 | ecm -n -c 17748 11e7

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