Contribution and Reservation

3·10¹⁹²-1 =: 2(9)₁₉₂_<193>; = 179209 · 592154051319954517820401873_<27> · 294029254151558642128613500432031_<33> · [96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497_<128>] (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=53705871 for P33) SUBMIT/RESERVE

Status

Expression:	3·10¹⁹²-1
Composite Factor:	961471003447140939858801657901425087137909384545540917288200 583110928859188099608538954694727738627733014327995363809611 32175497 (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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 192.48-digit and the GNFS difficulty is 127.98-digit. GNFS must be faster than SNFS. It will take about 5 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of GNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 29999_192.
Put the following polynomial file 29999_192.poly in there too.
And then, run "perl factMsieve.pl 29999_192".

29999_192.poly

# Murphy_E = 9.470857e-11, selected by Jeff Gilchrist
n: 96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497
Y0: -4728337515127376913733073
Y1: 113391337021723
c0: -68746208699076990334683890878800
c1: 2556257913066612300971980446
c2: -15170833482453671465739
c3: -20681738268242644
c4: 50385102936
c5: 40680
skew: 464131.78
type: gnfs
# selected mechanically
rlim: 8600000
alim: 8600000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=5*10^(d/20-5)[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 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	500	Erik Branger	Jan 31, 2009
		1850	Wataru Sakai	Nov 27, 2009
		2350 / 2350
45	11e6	0 / 3961
45	11e6	/ 3961
50	43e6	0 / 7465 (1129)
50	43e6	/ 7465 (1129)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497 | ecm -n -c 3961 11e6

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

echo 96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497 | ecm -n -c 7465 43e6

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

echo 96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497 | ecm -n -c 17751 11e7

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

echo 96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

NFS

Steps of GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation