M2304691 Mersenne number exponent details

Residue

Status

L-L

2F333001C4E0F3CB

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	12.8928	67.1642%	5000000	505000000	3.1582	10.9723%	16.0510	70.7670%	3.6029%
PrimeNet	2⁵⁸	0.0167	62.0690%	10000	190000	0.0019	2.9291%	0.0186	63.1800%	1.1110%
GPU72	2⁶²	0.2666	64.5161%	12000	200000	0.0022	1.7382%	0.2687	65.1329%	0.6168%
Difference	+5	+12.6262	+2.6481%	+4988000	+504800000	+3.1560	+9.2341%	+15.7823	+5.6341%	+5.6341%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.8928

67.1642%

5000000

505000000

3.1582

10.9723%

16.0510

70.7670%

3.6029%

PrimeNet

2⁵⁸

0.0167

62.0690%

10000

190000

0.0019

2.9291%

0.0186

63.1800%

1.1110%

GPU72

2⁶²

0.2666

64.5161%

12000

200000

0.0022

1.7382%

0.2687

65.1329%

0.6168%

Difference

+12.6262

+2.6481%

+4988000

+504800000

+3.1560

+9.2341%

+15.7823

+5.6341%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2304691	30350919701657570736673	23	74.684	6584596308498096 2⁴ × 3² × 7 × 29 × 225253020953	2017-08-23	29	225253020953	2,837.2	1,202.2	2,245.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2304691

30350919701657570736673

74.684

6584596308498096
2⁴ × 3² × 7 × 29 × 225253020953

2017-08-23

225253020953

2,837.2

1,202.2

2,245.3

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.284%
2010-02-15T08:09:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.821%
2018-02-18T15:36:11	alpertron	Manual testing	500000	15000000	12	-		-	-	0.126	-	-	5.211%
2021-06-10T01:33:22	ViliamF	3	5000000	505000000		-		-	-	3.158	-	-	10.972%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:11	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.050	-	-
2009-01-15T01:08:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-12T19:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-12-06T02:46:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.426	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.852	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.621	-	-
2015-10-21T10:28:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.242	-	-
2017-05-31T02:32:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.485	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.567 GHz-days
Estimated T-Level:	1.450

Digits	B1	Curves	Complete	FacMiss
20	11000	29 / 100	0.290	74.717%
25	50000	29 / 280	0.104	90.144%

New Calculation Method

Total ECM effort:	2.567 GHz-days
Estimated T-Level:	1.450

Digits	B1	Complete	FacMiss
20	11000	0.935	39.240%
25	50000	0.085	91.893%
30	250000	0.005	99.481%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.390
50000	5000000	30350919701657570736673	2	0.177

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-19T05:03:00	bayanne	MacBook	50000	5000000						3	0.266
2010-01-11T05:48:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.266
2011-11-25T19:32:00	S36049	Wolle5	50000	5000000						3	0.266
2013-09-28T19:26:00	Bruce	apandya-DESK11	50000	5000000						3	0.266
2015-04-14T15:33:00	Jason U	Server7	50000	5000000						3	0.266
2016-02-14T13:22:08	Sintax	cloud2	50000	5000000						3	0.266
2016-04-19T19:02:17	Bruce	Desk6	50000	5000000						3	0.266
2016-08-07T17:50:49	Bruce	Desk6	50000	5000000						3	0.266
2017-01-10T05:24:35	Bruce	Desk6	50000	5000000						3	0.266
2017-08-23T15:25:36	Bruce	Desk6	50000	5000000	30350919701657570736673	74.684	2	2		2	0.177

date	userid	compid	res64	spent (GHz-days)
1998-02-19T00:00:00	ANONYMOUS	v4_computers	2F333001C4E0F3CB	0.156
1999-06-15T00:00:00	ANONYMOUS	v4_computers	2F333001C4E0F3CB	0.156

date

userid

compid

res64

spent (GHz-days)

1998-02-19T00:00:00

ANONYMOUS

v4_computers

2F333001C4E0F3CB

0.156

1999-06-15T00:00:00

ANONYMOUS

v4_computers

2F333001C4E0F3CB

0.156

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 = 5000000, B2 = 505000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

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

B1 = 500000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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