Contribution and Reservation

(64·10²⁵⁹-1)/9 =: 7(1)₂₅₉_<260>; = 4001 · 3597511 · 56713351 · [87112699794359042586451253703975665319083031916075724219400771768164741981363134854094062140245932130962168088838928660801926822756005231002955716384634756576629261292393792113267102046095288546551305725724873251496971734277833264103453057751_<242>] SUBMIT/RESERVE

Status

Expression:	(64·10²⁵⁹-1)/9
Composite Factor:	871126997943590425864512537039756653190830319160757242194007 717681647419813631348540940621402459321309621680888389286608 019268227560052310029557163846347565766292612923937921132671 020460952885465513057257248732514969717342778332641034530577 51 (242-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 260.81-digit and the GNFS difficulty is 241.94-digit. SNFS must be faster than GNFS. It will take about 2057 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 71111_259.
Put the following polynomial file 71111_259.poly in there too.
And then, run "perl factMsieve.pl 71111_259".

71111_259.poly ^*1

n: 87112699794359042586451253703975665319083031916075724219400771768164741981363134854094062140245932130962168088838928660801926822756005231002955716384634756576629261292393792113267102046095288546551305725724873251496971734277833264103453057751
m: 20000000000000000000000000000000000000000000
deg: 6
c6: 10
c0: -1
skew: 0.68
type: snfs
lss: 1
rlim: 156000000
alim: 156000000
lpbr: 31
lpba: 31
mfbr: 63
mfba: 63
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 242-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	450	Serge Batalov	Jan 25, 2009
		23	Serge Batalov	Jan 27, 2009
		473 / 473
45	11e6	540	Serge Batalov	Jan 27, 2009
		540 / 4374
		/ 3834
50	43e6	0 / 7414 (1093)
50	43e6	/ 7414 (1093)
55	11e7	0 / 17732 (3076)
55	11e7	/ 17732 (3076)
60	26e7	0 / 42008 (7627)
60	26e7	/ 42008 (7627)

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

echo 87112699794359042586451253703975665319083031916075724219400771768164741981363134854094062140245932130962168088838928660801926822756005231002955716384634756576629261292393792113267102046095288546551305725724873251496971734277833264103453057751 | ecm -n -c 3834 11e6

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

echo 87112699794359042586451253703975665319083031916075724219400771768164741981363134854094062140245932130962168088838928660801926822756005231002955716384634756576629261292393792113267102046095288546551305725724873251496971734277833264103453057751 | ecm -n -c 7414 43e6

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

echo 87112699794359042586451253703975665319083031916075724219400771768164741981363134854094062140245932130962168088838928660801926822756005231002955716384634756576629261292393792113267102046095288546551305725724873251496971734277833264103453057751 | ecm -n -c 17732 11e7

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

echo 87112699794359042586451253703975665319083031916075724219400771768164741981363134854094062140245932130962168088838928660801926822756005231002955716384634756576629261292393792113267102046095288546551305725724873251496971734277833264103453057751 | ecm -n -c 42008 26e7

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