Contribution and Reservation

10²⁵⁰+3 =: 1(0)₂₄₉3_<251>; = 7 · 43 · [33222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269103_<248>] RESERVED

Status

Expression:	10²⁵⁰+3
Composite Factor:	332225913621262458471760797342192691029900332225913621262458 471760797342192691029900332225913621262458471760797342192691 029900332225913621262458471760797342192691029900332225913621 262458471760797342192691029900332225913621262458471760797342 19269103 (248-digit)
Status:	Not factored. Reserved by Lionel Debroux 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 250.00-digit and the GNFS difficulty is 247.52-digit. SNFS must be faster than GNFS. It will take about 898 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 10003_250.
Put the following polynomial file 10003_250.poly in there too.
And then, run "perl factMsieve.pl 10003_250".

10003_250.poly

n: 33222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269103
m: 100000000000000000000000000000000000000000
deg: 6
c6: 10000
c0: 3
skew: 0.26
type: snfs
lss: 1
rlim: 103000000
alim: 103000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.8
alambda: 2.8

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 248-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	20	Serge Batalov	Dec 16, 2008
		60	Serge Batalov	Dec 19, 2008
		2200	Serge Batalov	Dec 31, 2008
		2280 / 747
50	43e6	1000	yoyo@home	Jan 15, 2010
		1000 / 7003
		/ 6003
55	11e7	0 / 17262 (2491)
55	11e7	/ 17262 (2491)
60	26e7	0 / 41863 (7425)
60	26e7	/ 41863 (7425)
65	85e7	0 / 69378 (13561)
65	85e7	/ 69378 (13561)

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

echo 33222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269103 | ecm -n -c 6003 43e6

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

echo 33222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269103 | ecm -n -c 17262 11e7

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

echo 33222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269103 | ecm -n -c 41863 26e7

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

echo 33222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269102990033222591362126245847176079734219269103 | ecm -n -c 69378 85e7

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