Contribution and Reservation

(82·10¹⁷⁸-1)/9 =: 9(1)₁₇₈_<179>; = 431 · 2027843 · 69687221 · 1199011957379_<13> · 509829327232989091617649_<24> · [2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837_<127>] SUBMIT/RESERVE

Status

Expression:	(82·10¹⁷⁸-1)/9
Composite Factor:	244713692740507078389991040018567943646336804856718680583181 623155424857760054328459772400587761717157008959794862192553 6285837 (127-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 181.61-digit and the GNFS difficulty is 126.39-digit. GNFS may be faster than SNFS. It will take about 4 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 91111_178.
Put the following polynomial file 91111_178.poly in there too.
And then, run "perl factMsieve.pl 91111_178".

91111_178.poly ^*1

# Murphy_E = 1.232134e-10, selected by Jeff Gilchrist
n: 2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837
Y0: -2369529150349378980128455
Y1: 47862860182511
c0: 232678753995997350188832252107232
c1: 10325331511197178898573571616
c2: -8444053540704336255914
c3: -41048977619589689
c4: 15305847174
c5: 32760
skew: 709302.38
type: gnfs
# selected mechanically
rlim: 7800000
alim: 7800000
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 127-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 15, 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 2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837 | ecm -n -c 1850 3e6

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

echo 2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837 | ecm -n -c 4370 11e6

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

echo 2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837 | ecm -n -c 7535 43e6

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

echo 2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837 | 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