M2277389 Mersenne number exponent details

Residue

Status

L-L

1E154A445AE747E7

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	13.0474	67.1642%	391910	14198195	0.1091	4.9993%	13.1564	68.8057%	1.6416%
PrimeNet	2⁵⁸	0.0169	62.0690%	10000	190000	0.0019	2.9227%	0.0187	63.1776%	1.1086%
GPU72	2⁶²	0.2698	64.5161%	12000	190000	0.0021	1.7088%	0.2718	65.1225%	0.6064%
Difference	+5	+12.7776	+2.6481%	+379910	+14008195	+0.1070	+3.2905%	+12.8846	+3.6833%	+3.6833%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.0474

67.1642%

391910

14198195

0.1091

4.9993%

13.1564

68.8057%

1.6416%

PrimeNet

2⁵⁸

0.0169

62.0690%

10000

190000

0.0019

2.9227%

0.0187

63.1776%

1.1086%

GPU72

2⁶²

0.2698

64.5161%

12000

190000

0.0021

1.7088%

0.2718

65.1225%

0.6064%

Difference

+12.7776

+2.6481%

+379910

+14008195

+0.1070

+3.2905%

+12.8846

+3.6833%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2277389	19126569374217667930033	23	74.018	4199231965689144 2³ × 3² × 43 × 937187 × 1447247	2016-07-27	937187	1447247	1,819.6	0.0920	0.1818

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2277389

19126569374217667930033

74.018

4199231965689144
2³ × 3² × 43 × 937187 × 1447247

2016-07-27

937187

1447247

1,819.6

0.0920

0.1818

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.283%
2010-11-06T16:27:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.241%
2010-11-14T13:24:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.422%
2011-01-01T03:49:00	markr	tiny	105000	2152500		-		-	-	0.021	-	-	2.759%
2014-09-15T22:12:00	ANONYMOUS	Manual testing	133183	133183		-		-	-	0.013	-	-	1.094%
2016-03-20T01:38:11	Jocelyn Larouche	Manual testing	272160	272160		-		-	-	0.026	-	-	1.572%
2016-04-02T11:41:51	Jocelyn Larouche	Manual testing	326592	326592		-		-	-	0.031	-	-	1.710%
2016-04-07T01:57:18	Jocelyn Larouche	Manual testing	391910	7054380	12	-		-	-	0.072	-	-	4.361%
2016-04-15T01:15:40	Jocelyn Larouche	Manual testing	391910	14198195	12	-		-	-	0.109	-	-	4.999%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:10	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-15T02:55:00	Sturle Sunde	gnom.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-06T18:06:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.135	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.431	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.862	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.641	-	-
2015-11-01T21:51:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.281	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.978 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:	1.978 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	1.806
50000	5000000	19126569374217667930033	2	0.172

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-09T05:31:00	Never Odd Or Even	G_Quad	50000	5000000						3	0.258
2010-01-03T16:45:00	James Classen	towerofart	50000	5000000						3	0.258
2011-11-07T15:47:00	S36049	Wolle5	50000	5000000						3	0.258
2013-08-30T20:53:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.258
2015-04-07T13:38:00	Bruce	desk16	50000	5000000						3	0.258
2016-02-12T18:17:18	S36049	Wolle4	50000	5000000						3	0.258
2016-04-08T08:04:15	Bruce	Desk6	50000	5000000						3	0.258
2016-07-27T11:35:17	Bruce	Desk6	50000	5000000	19126569374217667930033	74.018	2	2		2	0.172

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	1E154A445AE747E7	0.150

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

1E154A445AE747E7

0.150

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 = 391910, B2 = 14198195 (P-1 stage 2)

B1 = 391910, B2 = 7054380 (P-1 stage 2)

B1 = 391910 (P-1 stage 1)

B1 = 326592 (P-1 stage 1)

B1 = 272160 (P-1 stage 1)

B1 = 105000, B2 = 2152500 (P-1 stage 2)

B1 = 133183 (P-1 stage 1)

B1 = 105000 (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)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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