M2296237 Mersenne number exponent details

Residue

Status

L-L

E330A82D75AF1314

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	12.9403	67.1642%	431337	4313370	0.0630	3.9645%	13.0032	68.4659%	1.3018%
PrimeNet	2⁵⁸	0.0167	62.0690%	10000	190000	0.0019	2.9271%	0.0187	63.1793%	1.1103%
GPU72	2⁶²	0.2676	64.5161%	12000	200000	0.0022	1.7370%	0.2697	65.1325%	0.6163%
Difference	+5	+12.6727	+2.6481%	+419337	+4113370	+0.0608	+2.2275%	+12.7335	+3.3335%	+3.3335%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.9403

67.1642%

431337

4313370

0.0630

3.9645%

13.0032

68.4659%

1.3018%

PrimeNet

2⁵⁸

0.0167

62.0690%

10000

190000

0.0019

2.9271%

0.0187

63.1793%

1.1103%

GPU72

2⁶²

0.2676

64.5161%

12000

200000

0.0022

1.7370%

0.2697

65.1325%

0.6163%

Difference

+12.6727

+2.6481%

+419337

+4113370

+0.0608

+2.2275%

+12.7335

+3.3335%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2296237	60687489272289626506684073	26	85.650	13214552607655400228 2² × 271 × 283 × 43076136699749	2018-01-15	283	43076136699749	5,456,925	229,893	429,375

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2296237

60687489272289626506684073

85.650

13214552607655400228
2² × 271 × 283 × 43076136699749

2018-01-15

283

43076136699749

5,456,925

229,893

429,375

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.284%
2010-11-07T12:40:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.241%
2010-11-15T02:50:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.308%
2010-12-03T15:05:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.786%
2011-01-17T15:22:00	Oscar Östlin		85000	1742500		-		-	-	0.017	-	-	2.523%
2014-06-11T02:10:00	Jocelyn Larouche	Manual testing	112952	112952		-		-	-	0.011	-	-	1.000%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	140904	140904		-		-	-	0.014	-	-	1.129%
2016-01-25T11:47:50	Jocelyn Larouche	Manual testing	431337	4313370	6	-		-	-	0.063	-	-	3.964%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-16T19:02:00	Sturle Sunde	hummel.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-12T06:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.134	-	-
2013-12-06T02:47:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.428	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.855	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.627	-	-
2015-11-04T09:56:27	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.254	-	-
2017-05-27T13:18:46	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.509	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.742 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	2.742 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.090	91.358%
30	250000	0.006	99.445%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.654
50000	5000000	60687489272289626506684073	1	0.088

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-19T18:44:00	Johan Koolwaaij	C0B5A3B75	50000	5000000						3	0.265
2010-01-07T07:17:00	SubPrime	abd0	50000	5000000						3	0.265
2011-11-18T11:08:00	S36049	Wolle5	50000	5000000						3	0.265
2013-09-18T16:54:00	arnaud	srv-630	50000	5000000						3	0.265
2015-04-11T19:33:00	Syntony	Hadfield	50000	5000000						3	0.265
2016-02-14T11:54:47	DominicB	starwalker	50000	5000000						3	0.265
2016-04-16T20:12:53	Bruce	Desk6	50000	5000000						3	0.265
2016-08-03T21:15:07	Bruce	Desk6	50000	5000000						3	0.265
2017-01-03T09:01:43	Bruce	Desk6	50000	5000000						3	0.265
2017-08-12T01:17:25	Bruce	Desk6	50000	5000000						3	0.265
2018-01-15T15:34:21	Bruce	Desk6	50000	5000000	60687489272289626506684073	85.650	1	2		1	0.088

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	E330A82D75AF1314	0.155

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

E330A82D75AF1314

0.155

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 = 431337, B2 = 4313370 (P-1 stage 2)

B1 = 431337 (P-1 stage 1)

B1 = 85000, B2 = 1742500 (P-1 stage 2)

B1 = 140904 (P-1 stage 1)

B1 = 112952 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 20000 (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

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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