Contribution and Reservation

8·10²²⁴-1 =: 7(9)₂₂₄_<225>; = 6529 · 12856873 · 358517287 · [26582624898088268458525485967685533114726102247032184064107102154612767510843394647982313692126079274668399015903173143391066945589480108775802488297230318786644603729866945298075686177706304423005631346881_<206>] SUBMIT/RESERVE

Status

Expression:	8·10²²⁴-1
Composite Factor:	265826248980882684585254859676855331147261022470321840641071 021546127675108433946479823136921260792746683990159031731433 910669455894801087758024882972303187866446037298669452980756 86177706304423005631346881 (206-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 225.20-digit and the GNFS difficulty is 205.42-digit. SNFS must be faster than GNFS. It will take about 134 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 79999_224.
Put the following polynomial file 79999_224.poly in there too.
And then, run "perl factMsieve.pl 79999_224".

79999_224.poly ^*1

n: 26582624898088268458525485967685533114726102247032184064107102154612767510843394647982313692126079274668399015903173143391066945589480108775802488297230318786644603729866945298075686177706304423005631346881
m: 20000000000000000000000000000000000000
deg: 6
c6: 25
c0: -2
skew: 0.66
type: snfs
lss: 1
rlim: 40000000
alim: 40000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
rlambda: 2.7
alambda: 2.7

*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 206-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	904	Serge Batalov	Sep 9, 2008
35	1e6	904 / 825
40	3e6	0 / 2089
40	3e6	/ 2089
45	11e6	0 / 4437 (606)
45	11e6	/ 4437 (606)
50	43e6	0 / 7548 (1265)
50	43e6	/ 7548 (1265)
55	11e7	0 / 17769 (3131)
55	11e7	/ 17769 (3131)

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

echo 26582624898088268458525485967685533114726102247032184064107102154612767510843394647982313692126079274668399015903173143391066945589480108775802488297230318786644603729866945298075686177706304423005631346881 | ecm -n -c 2089 3e6

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

echo 26582624898088268458525485967685533114726102247032184064107102154612767510843394647982313692126079274668399015903173143391066945589480108775802488297230318786644603729866945298075686177706304423005631346881 | ecm -n -c 4437 11e6

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

echo 26582624898088268458525485967685533114726102247032184064107102154612767510843394647982313692126079274668399015903173143391066945589480108775802488297230318786644603729866945298075686177706304423005631346881 | ecm -n -c 7548 43e6

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

echo 26582624898088268458525485967685533114726102247032184064107102154612767510843394647982313692126079274668399015903173143391066945589480108775802488297230318786644603729866945298075686177706304423005631346881 | ecm -n -c 17769 11e7

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