M1112341 Mersenne number exponent details

Residue

Status

L-L

30DA144F29EDE6F1

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	26.7130	68.6567%	500000	10000000	0.0437	4.4086%	26.7567	70.0385%	1.3818%
PrimeNet	2⁵⁶	0.0086	62.5000%	4500	70000	0.0003	2.0783%	0.0090	63.2794%	0.7794%
GPU72	2⁶⁰	0.1381	65.0000%	4500	22000	0.0002	0.6856%	0.1383	65.2400%	0.2400%
Difference	+7	+26.5749	+3.6567%	+495500	+9978000	+0.0435	+3.7230%	+26.6184	+4.7986%	+4.7986%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

26.7130

68.6567%

500000

10000000

0.0437

4.4086%

26.7567

70.0385%

1.3818%

PrimeNet

2⁵⁶

0.0086

62.5000%

4500

70000

0.0003

2.0783%

0.0090

63.2794%

0.7794%

GPU72

2⁶⁰

0.1381

65.0000%

4500

22000

0.0002

0.6856%

0.1383

65.2400%

0.2400%

Difference

+26.5749

+3.6567%

+495500

+9978000

+0.0435

+3.7230%

+26.6184

+4.7986%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1112341	4386272891280444099202777	25	81.859	1971640392325934268 2² × 3 × 139 × 1182038604511951	2013-12-08	139	1182038604511951	507,743	2,767,711	5,169,313

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1112341

4386272891280444099202777

81.859

1971640392325934268
2² × 3 × 139 × 1182038604511951

2013-12-08

139

1182038604511951

507,743

2,767,711

5,169,313

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-10T00:00:00	Jocelyn Larouche	v4_computers	15000	168750		-		-	-	0.001	-	-	0.706%
2012-10-23T08:44:00	kurly	smile	500000	10000000		-		-	-	0.044	-	-	4.409%
2016-03-17T19:00:00	alpertron	Manual testing	300000	10000000	12	-		-	-	0.036	-	-	4.121%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-12-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.017	-	-
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.035	-	-
2022-03-07T17:30:51	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.104	-	-
2009-01-14T17:21:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.138	-	-
2011-05-09T14:44:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.276	-	-
2012-10-11T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.883	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.592 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	323 / 100	3.230	3.892%
25	50000	323 / 280	1.154	31.486%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.592 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.731	0.000%
25	50000	1.613	19.937%
30	250000	0.131	87.717%
35	1000000	0.009	99.131%

ECM Summary

B1	B2	factor	curves	GHz-days
		4386272891280444099202777	1	0.00000e+0
50000	5000000		279	9.84
250000	25000000		44	7.756

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-04T14:37:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-04-28T06:32:00	Scott Kurowski	LM-Dell4600	50000	5000000						3	0.106
2008-12-14T19:40:00	Sturle Sunde	v21	50000	5000000						3	0.106
2009-04-12T07:23:00	mdrg	MDRG02	50000	5000000						3	0.106
2009-09-03T00:31:00	Lupo	yorick	50000	5000000						3	0.106
2009-12-04T15:03:00	KayJongsma	Wolter1	50000	5000000						3	0.106
2010-05-05T18:43:00	Geoff Wing	GW1	50000	5000000						3	0.106
2011-02-09T06:54:00	James Hintz	nana	50000	5000000						3	0.106
2011-10-15T21:28:00	Lukasz Wrobel	4_core_L	50000	5000000						3	0.106
2012-06-08T01:23:00	OS1	Tina	50000	5000000						3	0.106
2012-10-08T03:05:00	ANONYMOUS		50000	5000000						3	0.106
2013-05-23T21:09:00	OS1	Tina	50000	5000000						3	0.106
2013-12-08T13:23:00	jim f in mn	asus			4386272891280444099202777	81.859		1		1	-
2017-06-02T16:29:26	TJAOI	Manual testing	50000	5000000						104	3.666
2018-03-09T17:09:20	TJAOI	Manual testing	50000	5000000						141	4.971
2020-08-21T10:50:46	TJAOI	Manual testing	250000	25000000						44	7.756

date	userid	compid	res64	spent (GHz-days)
2002-04-28T00:00:00	ANONYMOUS	v4_computers	30DA144F29EDE6F1	0.033

date

userid

compid

res64

spent (GHz-days)

2002-04-28T00:00:00

ANONYMOUS

v4_computers

30DA144F29EDE6F1

0.033

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 15000, B2 = 168750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront