Contribution and Reservation

(4·10²¹³-1)/3 =: 1(3)₂₁₃_<214>; = 31 · 43 · 42929 · 1647001 · 55070453 · 109103879 · 315971342878788876787_<21> · 2472176201488989163470538770710003_<34> · [3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667_<130>] (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=1419575307 for P34 / Jul 15, 2008) SUBMIT/RESERVE

Status

Expression:	(4·10²¹³-1)/3
Composite Factor:	301424115125848225064662943094347430770926729059538081807026 601033560774832647337330520692605383195037453042378961159960 8439806667 (130-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 213.90-digit and the GNFS difficulty is 129.48-digit. GNFS must be faster than SNFS. It will take about 6 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 13333_213.
Put the following polynomial file 13333_213.poly in there too.
And then, run "perl factMsieve.pl 13333_213".

13333_213.poly ^*1

# Murphy_E = 8.216878e-11, selected by Jeff Gilchrist
n: 3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667
Y0: -9084369826382309550404707
Y1: 198544596610957
c0: -319029248223927563154255586152
c1: 37297736766201535368880422
c2: 272179889827118037343
c3: -24620985055955059
c4: -17017695293
c5: 48720
skew: 137963.59
type: gnfs
# selected mechanically
rlim: 9500000
alim: 9500000
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 130-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	2336	Wataru Sakai	Apr 29, 2009
40	3e6	2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
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 3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667 | ecm -n -c 3962 11e6

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

echo 3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667 | ecm -n -c 7465 43e6

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

echo 3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667 | ecm -n -c 17751 11e7

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

echo 3014241151258482250646629430943474307709267290595380818070266010335607748326473373305206926053831950374530423789611599608439806667 | ecm -n -c 42014 26e7

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