Contribution and Reservation

(8·10¹⁸²-17)/9 =: (8)₁₈₁7_<182>; = 3 · 47 · 29443147 · 245690237799029_<15> · 1409781315068910934903369464751_<31> · [61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339_<128>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=109125358 for P31 / Nov 14, 2008) SUBMIT/RESERVE

Status

Expression:	(8·10¹⁸²-17)/9
Composite Factor:	618165106364244025563227513160696046848102863688110271480556 457385871352639149504921935687455105184278671181285010161673 99497339 (128-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.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 182.90-digit and the GNFS difficulty is 127.79-digit. GNFS may be faster than SNFS. It will take about 5 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 88887_182.
Put the following polynomial file 88887_182.poly in there too.
And then, run "perl factMsieve.pl 88887_182".

88887_182.poly ^*1

# Murphy_E = 1.048601e-10, selected by Jeff Gilchrist
n: 61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339
Y0: -4447632518565105901260533
Y1: 126137962925689
c0: -8122383434596789707492715406100
c1: 144879329951276193842306928
c2: -44030319988620292887
c3: -10102513412965018
c4: -37358725208
c5: 35520
skew: 255169.49
type: gnfs
# selected mechanically
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 128-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	0 / 0
40	3e6	500	Erik Branger	Feb 14, 2009
		500 / 2350
		/ 1850
45	11e6	0 / 4370 (537)
45	11e6	/ 4370 (537)
50	43e6	0 / 7535 (1246)
50	43e6	/ 7535 (1246)
55	11e7	0 / 17766 (3126)
55	11e7	/ 17766 (3126)

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

echo 61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339 | ecm -n -c 1850 3e6

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

echo 61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339 | ecm -n -c 4370 11e6

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

echo 61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339 | ecm -n -c 7535 43e6

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

echo 61816510636424402556322751316069604684810286368811027148055645738587135263914950492193568745510518427867118128501016167399497339 | ecm -n -c 17766 11e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation