Contribution and Reservation

4·10²⁰²+1 =: 4(0)₂₀₁1_<203>; = 13 · 53 · 401 · 57046808129_<11> · [2537844725803420328887628871520761614880751052460146328527456957132886335150680835789893810531480123336261822484061148938746550767856006587355156604026683746870394258989020154920033813121_<187>] SUBMIT/RESERVE

Status

Expression:	4·10²⁰²+1
Composite Factor:	253784472580342032888762887152076161488075105246014632852745 695713288633515068083578989381053148012333626182248406114893 874655076785600658735515660402668374687039425898902015492003 3813121 (187-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 202.90-digit and the GNFS difficulty is 186.40-digit. SNFS must be faster than GNFS. It will take about 24 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_202.
Put the following polynomial file 40001_202.poly in there too.
And then, run "perl factMsieve.pl 40001_202".

40001_202.poly ^*1

n: 2537844725803420328887628871520761614880751052460146328527456957132886335150680835789893810531480123336261822484061148938746550767856006587355156604026683746870394258989020154920033813121
m: 20000000000000000000000000000000000000000
deg: 5
c5: 25
c0: 2
skew: 0.60
type: snfs
lss: 1
rlim: 16900000
alim: 16900000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
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 187-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 2537844725803420328887628871520761614880751052460146328527456957132886335150680835789893810531480123336261822484061148938746550767856006587355156604026683746870394258989020154920033813121 | ecm -n -c 825 1e6

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

echo 2537844725803420328887628871520761614880751052460146328527456957132886335150680835789893810531480123336261822484061148938746550767856006587355156604026683746870394258989020154920033813121 | ecm -n -c 2336 3e6

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

echo 2537844725803420328887628871520761614880751052460146328527456957132886335150680835789893810531480123336261822484061148938746550767856006587355156604026683746870394258989020154920033813121 | ecm -n -c 4479 11e6

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

echo 2537844725803420328887628871520761614880751052460146328527456957132886335150680835789893810531480123336261822484061148938746550767856006587355156604026683746870394258989020154920033813121 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers