Contribution and Reservation

4·10²⁵⁰+1 =: 4(0)₂₄₉1_<251>; = 13 · 3646063837616479765543282237_<28> · 609367039316849421092272000364917_<33> · [1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213_<190>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=3159199225 for P33 / Nov 2, 2008) (Wataru Sakai / GMP-ECM 6.2.1 B1=1000000, sigma=1542610798 for P28 / Feb 17, 2009) SUBMIT/RESERVE

Status

Expression:	4·10²⁵⁰+1
Composite Factor:	138488404291042016534740967879546596336353429695421224679668 447635621772888573663504337582618232542754316572402346627909 258582042052046553375035833947864027215825531703275938573102 5755994213 (190-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 252.00-digit and the GNFS difficulty is 189.14-digit. SNFS must be faster than GNFS. It will take about 1047 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 40001_250.
Put the following polynomial file 40001_250.poly in there too.
And then, run "perl factMsieve.pl 40001_250".

40001_250.poly ^*1

n: 1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213
m: 1000000000000000000000000000000000000000000
deg: 6
c6: 1
c0: 25
skew: 1.71
type: snfs
lss: 1
rlim: 111000000
alim: 111000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.8
alambda: 2.8

*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 190-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	2111	Wataru Sakai	Feb 21, 2009
40	3e6	2111 / 2111
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213 | ecm -n -c 3974 11e6

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

echo 1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213 | ecm -n -c 7469 43e6

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

echo 1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213 | ecm -n -c 17752 11e7

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

echo 1384884042910420165347409678795465963363534296954212246796684476356217728885736635043375826182325427543165724023466279092585820420520465533750358339478640272158255317032759385731025755994213 | ecm -n -c 42014 26e7

Submit factors

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