Contribution and Reservation

4·10²¹⁵+1 =: 4(0)₂₁₄1_<216>; = 7 · 23 · 53 · 1297201 · [36136906405573128456836083283356074588169542782615077068476073202232453553512225240515872685646938518198652624549390924625188636898700958827123610264233047893056133465118692496172550297971455671380039174797_<206>] SUBMIT/RESERVE

Status

Expression:	4·10²¹⁵+1
Composite Factor:	361369064055731284568360832833560745881695427826150770684760 732022324535535122252405158726856469385181986526245493909246 251886368987009588271236102642330478930561334651186924961725 50297971455671380039174797 (206-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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 216.30-digit and the GNFS difficulty is 205.56-digit. SNFS must be faster than GNFS. It will take about 68 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 40001_215.
Put the following polynomial file 40001_215.poly in there too.
And then, run "perl factMsieve.pl 40001_215".

40001_215.poly ^*1

n: 36136906405573128456836083283356074588169542782615077068476073202232453553512225240515872685646938518198652624549390924625188636898700958827123610264233047893056133465118692496172550297971455671380039174797
m: 1000000000000000000000000000000000000
deg: 6
c6: 2
c0: 5
skew: 1.16
type: snfs
lss: 1
rlim: 28000000
alim: 28000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 206-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-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
30	25e4	430	Makoto Kamada	Nov 3, 2008
30	25e4	430 / 430
35	1e6	0 / 825
35	1e6	/ 825
40	3e6	0 / 2336 (294)
40	3e6	/ 2336 (294)
45	11e6	0 / 4479 (677)
45	11e6	/ 4479 (677)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

Command line to find prime factors up to about 35-digit

echo 36136906405573128456836083283356074588169542782615077068476073202232453553512225240515872685646938518198652624549390924625188636898700958827123610264233047893056133465118692496172550297971455671380039174797 | ecm -n -c 825 1e6

Command line to find prime factors up to about 40-digit

echo 36136906405573128456836083283356074588169542782615077068476073202232453553512225240515872685646938518198652624549390924625188636898700958827123610264233047893056133465118692496172550297971455671380039174797 | ecm -n -c 2336 3e6

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

echo 36136906405573128456836083283356074588169542782615077068476073202232453553512225240515872685646938518198652624549390924625188636898700958827123610264233047893056133465118692496172550297971455671380039174797 | ecm -n -c 4479 11e6

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

echo 36136906405573128456836083283356074588169542782615077068476073202232453553512225240515872685646938518198652624549390924625188636898700958827123610264233047893056133465118692496172550297971455671380039174797 | ecm -n -c 7553 43e6

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