Contribution and Reservation

(64·10²⁷¹-1)/9 =: 7(1)₂₇₁_<272>; = 311 · 32693 · [6993946422458165190392105443096721896878041103138995713224460973544009795808783625186892728062784919307397791095344570266633388595345307909420132229955232076791083837342793432688680528296922575056983998080074282704952928172487154551911130283266741674556439273470157_<265>] SUBMIT/RESERVE

Status

Expression:	(64·10²⁷¹-1)/9
Composite Factor:	699394642245816519039210544309672189687804110313899571322446 097354400979580878362518689272806278491930739779109534457026 663338859534530790942013222995523207679108383734279343268868 052829692257505698399808007428270495292817248715455191113028 3266741674556439273470157 (265-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 272.81-digit and the GNFS difficulty is 264.84-digit. SNFS must be faster than GNFS. It will take about 5168 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_271.
Put the following polynomial file 71111_271.poly in there too.
And then, run "perl factMsieve.pl 71111_271".

71111_271.poly ^*1

n: 6993946422458165190392105443096721896878041103138995713224460973544009795808783625186892728062784919307397791095344570266633388595345307909420132229955232076791083837342793432688680528296922575056983998080074282704952928172487154551911130283266741674556439273470157
m: 2000000000000000000000000000000000000000000000
deg: 6
c6: 10
c0: -1
skew: 0.68
type: snfs
lss: 1
rlim: 250000000
alim: 250000000
lpbr: 31
lpba: 31
mfbr: 65
mfba: 65
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 265-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
40	3e6	450 / 438
45	11e6	550	Serge Batalov	Jan 27, 2009
		550 / 4379
		/ 3829
50	43e6	0 / 7413 (1092)
50	43e6	/ 7413 (1092)
55	11e7	0 / 17732 (3075)
55	11e7	/ 17732 (3075)
60	26e7	0 / 42008 (7627)
60	26e7	/ 42008 (7627)

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

echo 6993946422458165190392105443096721896878041103138995713224460973544009795808783625186892728062784919307397791095344570266633388595345307909420132229955232076791083837342793432688680528296922575056983998080074282704952928172487154551911130283266741674556439273470157 | ecm -n -c 3829 11e6

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

echo 6993946422458165190392105443096721896878041103138995713224460973544009795808783625186892728062784919307397791095344570266633388595345307909420132229955232076791083837342793432688680528296922575056983998080074282704952928172487154551911130283266741674556439273470157 | ecm -n -c 7413 43e6

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

echo 6993946422458165190392105443096721896878041103138995713224460973544009795808783625186892728062784919307397791095344570266633388595345307909420132229955232076791083837342793432688680528296922575056983998080074282704952928172487154551911130283266741674556439273470157 | ecm -n -c 17732 11e7

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

echo 6993946422458165190392105443096721896878041103138995713224460973544009795808783625186892728062784919307397791095344570266633388595345307909420132229955232076791083837342793432688680528296922575056983998080074282704952928172487154551911130283266741674556439273470157 | ecm -n -c 42008 26e7

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