M2212361 Mersenne number exponent details

Residue

Status

L-L

4B81682B324A5AAF

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	13.4309	67.1642%	2000000	65000000	0.5179	7.6502%	13.9488	69.6762%	2.5120%
PrimeNet	2⁵⁸	0.0174	62.0690%	10000	180000	0.0018	2.8660%	0.0192	63.1561%	1.0871%
GPU72	2⁶²	0.2777	64.5161%	11000	170000	0.0019	1.6018%	0.2796	65.0845%	0.5684%
Difference	+5	+13.1532	+2.6481%	+1989000	+64830000	+0.5160	+6.0483%	+13.6692	+4.5917%	+4.5917%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.4309

67.1642%

2000000

65000000

0.5179

7.6502%

13.9488

69.6762%

2.5120%

PrimeNet

2⁵⁸

0.0174

62.0690%

10000

180000

0.0018

2.8660%

0.0192

63.1561%

1.0871%

GPU72

2⁶²

0.2777

64.5161%

11000

170000

0.0019

1.6018%

0.2796

65.0845%

0.5684%

Difference

+13.1532

+2.6481%

+1989000

+64830000

+0.5160

+6.0483%

+13.6692

+4.5917%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2212361	1953220014586778825501351	25	80.692	441433386004087675 5² × 11² × 145928392067467	2016-07-05	121	145928392067467	191,057	757,989	1,415,712

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2212361

1953220014586778825501351

80.692

441433386004087675
5² × 11² × 145928392067467

2016-07-05

121

145928392067467

191,057

757,989

1,415,712

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.281%
2010-11-06T00:22:00	ANONYMOUS	Manual testing	15000	15000		-		-	-	0.001	-	-	0.239%
2010-11-10T11:27:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.419%
2011-01-08T06:36:00	markr	tiny	90000	1665000		-		-	-	0.017	-	-	2.510%
2013-11-13T18:49:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.097	-	-	4.797%
2015-11-14T20:39:29	Alexander Dubrovin	Manual testing	1500000	10000000	12	-		-	-	0.187	-	-	5.281%
2015-12-11T13:23:51	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.650%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:08	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.069	-	-
2009-01-03T08:02:00	Sturle Sunde	aalto.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2009-01-07T04:42:00	Sturle Sunde	hindemith.ifi	2⁶¹	2⁶²		-	-	0.139	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.444	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.887	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.689	-	-
2015-10-22T10:17:21	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.378	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.970 GHz-days
Estimated T-Level:	1.150

Digits	B1	Curves	Complete	FacMiss
20	11000	23 / 100	0.230	79.361%
25	50000	23 / 280	0.082	92.100%

New Calculation Method

Total ECM effort:	1.970 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.742	47.619%
25	50000	0.067	93.514%
30	250000	0.004	99.588%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	1.799
50000	5000000	1953220014586778825501351	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-13T04:03:00	Chang Chia-Tche	euler06	50000	5000000						3	0.257
2010-01-01T11:03:00	Wojciech Florek	perta	50000	5000000						3	0.257
2011-12-05T16:11:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.257
2013-06-20T19:12:00	ANONYMOUS	S	50000	5000000						3	0.257
2015-03-15T19:21:00	Jason U	Server7	50000	5000000						3	0.257
2016-01-22T19:29:23	Jason U	Server7	50000	5000000						3	0.257
2016-03-14T20:18:17	Bruce	Desk6	50000	5000000						3	0.257
2016-07-05T04:42:57	Bruce	test	50000	5000000	1953220014586778825501351	80.692	2	2		2	0.171

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	4B81682B324A5AAF	0.145

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

4B81682B324A5AAF

0.145

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 = 2000000, B2 = 65000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1500000, B2 = 10000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

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

B1 = 500000 (P-1 stage 1)

B1 = 90000, B2 = 1665000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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