Contribution and Reservation

(32·10¹⁹⁷-23)/9 =: 3(5)₁₉₆3_<198>; = 11 · 2333 · [13854793108972277424913515783640087112011672663194309143730489637047716773391869834218741205453592937519212701381582650335329289465594652049859936700913983382907514926374763494352006996670520031_<194>] SUBMIT/RESERVE

Status

Expression:	(32·10¹⁹⁷-23)/9
Composite Factor:	138547931089722774249135157836400871120116726631943091437304 896370477167733918698342187412054535929375192127013815826503 353292894655946520498599367009139833829075149263747634943520 06996670520031 (194-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 198.51-digit and the GNFS difficulty is 193.14-digit. SNFS must be faster than GNFS. It will take about 17 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 35553_197.
Put the following polynomial file 35553_197.poly in there too.
And then, run "perl factMsieve.pl 35553_197".

35553_197.poly ^*1

n: 13854793108972277424913515783640087112011672663194309143730489637047716773391869834218741205453592937519212701381582650335329289465594652049859936700913983382907514926374763494352006996670520031
m: 2000000000000000000000000000000000000000
deg: 5
c5: 100
c0: -23
skew: 0.75
type: snfs
lss: 1
rlim: 14200000
alim: 14200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*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 194-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-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
40	3e6	2507	Max Dettweiler	Apr 9, 2009
40	3e6	2507 / 2004
45	11e6	0 / 3869
45	11e6	/ 3869
50	43e6	0 / 7451 (1103)
50	43e6	/ 7451 (1103)
55	11e7	0 / 17749 (3091)
55	11e7	/ 17749 (3091)
60	26e7	0 / 42014 (7634)
60	26e7	/ 42014 (7634)

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

echo 13854793108972277424913515783640087112011672663194309143730489637047716773391869834218741205453592937519212701381582650335329289465594652049859936700913983382907514926374763494352006996670520031 | ecm -n -c 3869 11e6

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

echo 13854793108972277424913515783640087112011672663194309143730489637047716773391869834218741205453592937519212701381582650335329289465594652049859936700913983382907514926374763494352006996670520031 | ecm -n -c 7451 43e6

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

echo 13854793108972277424913515783640087112011672663194309143730489637047716773391869834218741205453592937519212701381582650335329289465594652049859936700913983382907514926374763494352006996670520031 | ecm -n -c 17749 11e7

Command line to find prime factors up to about 60-digit

echo 13854793108972277424913515783640087112011672663194309143730489637047716773391869834218741205453592937519212701381582650335329289465594652049859936700913983382907514926374763494352006996670520031 | ecm -n -c 42014 26e7

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