M2250263 Mersenne number exponent details

Residue

Status

L-L

0C83B489E6DDFF01

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	13.2046	67.1642%	589050	5890500	0.0837	4.3765%	13.2883	68.6012%	1.4370%
PrimeNet	2⁵⁸	0.0171	62.0690%	10000	190000	0.0019	2.9163%	0.0190	63.1751%	1.1062%
GPU72	2⁶²	0.2730	64.5161%	11000	190000	0.0020	1.6600%	0.2750	65.1052%	0.5890%
Difference	+5	+12.9316	+2.6481%	+578050	+5700500	+0.0817	+2.7165%	+13.0133	+3.4961%	+3.4961%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.2046

67.1642%

589050

5890500

0.0837

4.3765%

13.2883

68.6012%

1.4370%

PrimeNet

2⁵⁸

0.0171

62.0690%

10000

190000

0.0019

2.9163%

0.0190

63.1751%

1.1062%

GPU72

2⁶²

0.2730

64.5161%

11000

190000

0.0020

1.6600%

0.2750

65.1052%

0.5890%

Difference

+12.9316

+2.6481%

+578050

+5700500

+0.0817

+2.7165%

+13.0133

+3.4961%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2250263	624586879886355625777	21	69.081	138780862478376 2³ × 3 × 5782535936599	2016-12-03	8	5782535936599	84.521	30,036	56,099

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2250263

624586879886355625777

69.081

138780862478376
2³ × 3 × 5782535936599

2016-12-03

5782535936599

84.521

30,036

56,099

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-03T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.282%
2010-10-20T15:54:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.783%
2011-01-14T14:58:00	Oscar Östlin		85000	1636250		-		-	-	0.016	-	-	2.478%
2014-06-01T23:28:00	Jocelyn Larouche	Manual testing	113523	113523		-		-	-	0.011	-	-	0.999%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	142046	142046		-		-	-	0.014	-	-	1.130%
2016-01-17T15:05:41	Jocelyn Larouche	Manual testing	589050	5890500	6	-		-	-	0.084	-	-	4.376%

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		-	-	0.068	-	-
2009-01-11T09:33:00	Sturle Sunde	wright.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-04T09:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.137	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.436	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.872	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.660	-	-
2015-10-27T09:37:31	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.321	-	-
2017-01-05T21:20:48	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.642	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.233 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	2.233 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.093	91.162%
30	250000	0.006	99.418%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.061
50000	5000000	624586879886355625777	2	0.172

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-29T03:01:00	Nathan Slaven	q6600	50000	5000000						3	0.258
2010-05-05T16:25:00	James Hintz	nana	50000	5000000						3	0.258
2011-10-19T19:34:00	S36049	Wolle5	50000	5000000						3	0.258
2013-07-31T05:33:00	hiems	Laptop	50000	5000000						3	0.258
2015-03-29T10:57:00	Bruce	desk16	50000	5000000						3	0.258
2016-02-02T12:25:27	Jason U	Server7	50000	5000000						3	0.258
2016-03-29T11:13:13	Bruce	Desk6	50000	5000000						3	0.258
2016-07-17T22:24:26	Bruce	Desk6	50000	5000000						3	0.258
2016-12-04T03:56:18	Bruce	Desk6	50000	5000000	624586879886355625777	69.081	2	2		2	0.172

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	0C83B489E6DDFF01	0.148

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

0C83B489E6DDFF01

0.148

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 = 589050, B2 = 5890500 (P-1 stage 2)

B1 = 589050 (P-1 stage 1)

B1 = 85000, B2 = 1636250 (P-1 stage 2)

B1 = 142046 (P-1 stage 1)

B1 = 113523 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

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10³

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10¹³

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