Contribution and Reservation

(64·10²⁰⁰+53)/9 =: 7(1)₁₉₉7_<201>; = 3 · 197 · 409 · 268480211 · 571928806571317915240679_<24> · 45425151191961551645257751237_<29> · [421770346394040881599223239317298450802946294340995839267974962730470930298837048241962065571728944449656378052921086055949471332412531_<135>] (Yoichi Hanatani) SUBMIT/RESERVE

Status

Expression:	(64·10²⁰⁰+53)/9
Composite Factor:	421770346394040881599223239317298450802946294340995839267974 962730470930298837048241962065571728944449656378052921086055 949471332412531 (135-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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 201.81-digit and the GNFS difficulty is 134.63-digit. GNFS must be faster than SNFS. It will take about 11 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of GNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 71117_200.
Put the following polynomial file 71117_200.poly in there too.
And then, run "perl factMsieve.pl 71117_200".

71117_200.poly

# Murphy_E = 4.161365e-11, selected by Jeff Gilchrist
n: 421770346394040881599223239317298450802946294340995839267974962730470930298837048241962065571728944449656378052921086055949471332412531
Y0: -88607725630466487821451549
Y1: 1149062854130369
c0: -4538820565643969854431820522556672
c1: 17264980110916028980866942606
c2: 65934022131965234670651
c3: -77993894973175184
c4: -160436753562
c5: 77220
skew: 678963.5
type: gnfs
# selected mechanically
rlim: 13100000
alim: 13100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=5*10^(d/20-5)[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 135-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-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
45	11e6	3961	Wataru Sakai	Dec 19, 2009
45	11e6	3961 / 3961
50	43e6	0 / 6576
50	43e6	/ 6576
55	11e7	0 / 17503 (2728)
55	11e7	/ 17503 (2728)
60	26e7	0 / 41951 (7529)
60	26e7	/ 41951 (7529)
65	85e7	0 / 69398 (13590)
65	85e7	/ 69398 (13590)

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

echo 421770346394040881599223239317298450802946294340995839267974962730470930298837048241962065571728944449656378052921086055949471332412531 | ecm -n -c 6576 43e6

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

echo 421770346394040881599223239317298450802946294340995839267974962730470930298837048241962065571728944449656378052921086055949471332412531 | ecm -n -c 17503 11e7

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

echo 421770346394040881599223239317298450802946294340995839267974962730470930298837048241962065571728944449656378052921086055949471332412531 | ecm -n -c 41951 26e7

Command line to find prime factors up to about 65-digit

echo 421770346394040881599223239317298450802946294340995839267974962730470930298837048241962065571728944449656378052921086055949471332412531 | ecm -n -c 69398 85e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

NFS

Steps of GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation