Contribution and Reservation

4·10²²¹+9 =: 4(0)₂₂₀9_<222>; = 1380329 · 6586109027452037_<16> · [43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133_<200>] SUBMIT/RESERVE

Status

Expression:	4·10²²¹+9
Composite Factor:	439995731314127318212443103949574771650250401987391288699458 843698937589158847256928246459756902560035172938933033496465 487051767934629673234769270590094612018134216103758685924254 69990878490457169133 (200-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 222.30-digit and the GNFS difficulty is 199.64-digit. SNFS must be faster than GNFS. It will take about 107 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 40009_221.
Put the following polynomial file 40009_221.poly in there too.
And then, run "perl factMsieve.pl 40009_221".

40009_221.poly ^*1

n: 43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133
m: 10000000000000000000000000000000000000
deg: 6
c6: 2
c0: 45
skew: 1.68
type: snfs
lss: 1
rlim: 35000000
alim: 35000000
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 200-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	0 / 0
35	1e6	118	Makoto Kamada	Mar 2, 2009
		118 / 904
		/ 786
40	3e6	0 / 2318 (280)
40	3e6	/ 2318 (280)
45	11e6	0 / 4475 (672)
45	11e6	/ 4475 (672)
50	43e6	0 / 7553 (1276)
50	43e6	/ 7553 (1276)

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

echo 43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133 | ecm -n -c 786 1e6

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

echo 43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133 | ecm -n -c 2318 3e6

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

echo 43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133 | ecm -n -c 4475 11e6

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

echo 43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers