Contribution and Reservation

(55·10¹⁸⁶-1)/9 =: 6(1)₁₈₆_<187>; = 3 · 47 · 457 · 14431 · 2394664399_<10> · 75538185761_<11> · 1193841383094873736720482221_<28> · [30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127_<131>] SUBMIT/RESERVE

Status

Expression:	(55·10¹⁸⁶-1)/9
Composite Factor:	304320076127625921277407227161711711028599256939336407240036 959115117039917556471778156753223067508084544599551923484101 31047397127 (131-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 189.84-digit and the GNFS difficulty is 130.48-digit. GNFS must be faster than SNFS. It will take about 7 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 61111_186.
Put the following polynomial file 61111_186.poly in there too.
And then, run "perl factMsieve.pl 61111_186".

61111_186.poly ^*1

# Murphy_E = 6.653532e-11, selected by Jeff Gilchrist
n: 30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127
Y0: -15577273573146209665776506
Y1: 297692296275319
c0: -219739078460408925067011684484071
c1: -24260873678142118954039942
c2: 8341108626032587786947
c3: -7198912295874522
c4: -12048017912
c5: 33180
skew: 442353.27
type: gnfs
# selected mechanically
rlim: 10100000
alim: 10100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6

*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 131-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	Jan 30, 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 30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127 | ecm -n -c 1850 3e6

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

echo 30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127 | ecm -n -c 4370 11e6

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

echo 30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127 | ecm -n -c 7535 43e6

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

echo 30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127 | 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