Contribution and Reservation

(26·10²⁰²+1)/9 =: 2(8)₂₀₁9_<203>; = 7 · 43 · 33739 · 8179693 · 41316437 · 780868339 · 4999350253283_<13> · 1001553437158757072561_<22> · [2152815273424542897125727861475328690897625509797906118796457455136664996946843316058630955180514572528820942826446265156479648694967920623_<139>] SUBMIT/RESERVE

Status

Expression:	(26·10²⁰²+1)/9
Composite Factor:	215281527342454289712572786147532869089762550979790611879645 745513666499694684331605863095518051457252882094282644626515 6479648694967920623 (139-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 205.51-digit and the GNFS difficulty is 138.33-digit. GNFS must be faster than SNFS. It will take about 16 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 28889_202.
Put the following polynomial file 28889_202.poly in there too.
And then, run "perl factMsieve.pl 28889_202".

28889_202.poly ^*1

# Murphy_E = 2.192004e-11, selected by Jeff Gilchrist
n: 2152815273424542897125727861475328690897625509797906118796457455136664996946843316058630955180514572528820942826446265156479648694967920623
Y0: -453624284853012937072972959
Y1: 3215718387724127
c0: 18281169367428284331699483830360
c1: -1210235435937039236597554976
c2: 16882693169079558579220
c3: 69214631001639128
c4: -103355397123
c5: 112080
skew: 232793.08
type: gnfs
# selected mechanically
rlim: 16400000
alim: 16400000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
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 139-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	Mar 26, 2009
		1836	Wataru Sakai	Nov 25, 2009
		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 2152815273424542897125727861475328690897625509797906118796457455136664996946843316058630955180514572528820942826446265156479648694967920623 | ecm -n -c 3962 11e6

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

echo 2152815273424542897125727861475328690897625509797906118796457455136664996946843316058630955180514572528820942826446265156479648694967920623 | ecm -n -c 7465 43e6

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

echo 2152815273424542897125727861475328690897625509797906118796457455136664996946843316058630955180514572528820942826446265156479648694967920623 | ecm -n -c 17751 11e7

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

echo 2152815273424542897125727861475328690897625509797906118796457455136664996946843316058630955180514572528820942826446265156479648694967920623 | 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