M2403053 Mersenne number exponent details

Residue

Status

L-L

8B98ABB815617228

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	2⁷⁰	99.4363	68.5714%	3102822	43439508	0.5192	5.7703%	99.9555	70.3849%	1.8135%
PrimeNet	2⁵⁹	0.0320	62.7119%	10000	170000	0.0018	2.4802%	0.0338	63.6367%	0.9248%
GPU72	2⁶³	0.6642	65.0794%	10000	140000	0.0017	1.2752%	0.6658	65.5247%	0.4453%
Difference	+7	+98.7721	+3.4921%	+3092822	+43299508	+0.5175	+4.4951%	+99.2896	+4.8603%	+4.8603%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

99.4363

68.5714%

3102822

43439508

0.5192

5.7703%

99.9555

70.3849%

1.8135%

PrimeNet

2⁵⁹

0.0320

62.7119%

10000

170000

0.0018

2.4802%

0.0338

63.6367%

0.9248%

GPU72

2⁶³

0.6642

65.0794%

10000

140000

0.0017

1.2752%

0.6658

65.5247%

0.4453%

Difference

+98.7721

+3.4921%

+3092822

+43299508

+0.5175

+4.4951%

+99.2896

+4.8603%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2403053	7360979153870570619367	22	72.640	1531589014863711 3² × 43 × 72019 × 54952087	2020-07-14	72019	54952087	407.53	0.2999	0.5478

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2403053

7360979153870570619367

72.640

1531589014863711
3² × 43 × 72019 × 54952087

2020-07-14

72019

54952087

407.53

0.2999

0.5478

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.150%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.140%
2010-11-16T23:08:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.183%
2010-12-22T22:53:00	markr	tiny	95000	1923750		-		-	-	0.019	-	-	1.849%
2014-02-19T05:39:00	mikr	MSI	3102822	43439508		-		-	-	0.519	-	-	5.770%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:13	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.064	-	-
2009-01-16T02:30:00	Sturle Sunde	gibus.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-
2012-06-03T10:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.128	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.409	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.817	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.555	-	-
2015-10-21T10:28:04	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.110	-	-
2017-06-29T16:14:23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.219	-	-
2019-01-25T12:45:36	Anton Repko	Manual testing	2⁶⁷	2⁶⁹		-	-	37.32	-	-
2019-02-04T05:43:01	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	49.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.609 GHz-days
Estimated T-Level:	3.150

Digits	B1	Curves	Complete	FacMiss
20	11000	63 / 100	0.630	53.091%
25	50000	63 / 280	0.225	79.819%

New Calculation Method

Total ECM effort:	5.609 GHz-days
Estimated T-Level:	3.150

Digits	B1	Complete	FacMiss
20	11000	2.032	13.104%
25	50000	0.184	83.221%
30	250000	0.011	98.875%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		62	5.520
50000	5000000	7360979153870570619367	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-30T17:09:00	S36049	Wolle3	50000	5000000						3	0.267
2010-02-19T05:35:00	Martti Järvi	TEMP	50000	5000000						3	0.267
2012-02-17T20:18:00	S36049	Wolle5	50000	5000000						3	0.267
2013-11-28T02:15:00	arnaud	srv-630	50000	5000000						3	0.267
2015-06-27T17:12:00	guru	w6	50000	5000000						3	0.267
2016-02-19T07:23:50	Sintax	cloud2	50000	5000000						3	0.267
2016-05-28T12:24:23	Bruce	Desk6	50000	5000000						3	0.267
2016-09-19T04:42:47	Bruce	Desk6	50000	5000000						3	0.267
2017-03-30T09:55:06	Bruce	Desk6	50000	5000000						3	0.267
2017-11-05T15:21:55	Bruce	Desk6	50000	5000000						3	0.267
2017-11-18T05:25:25	Sid & Andy	Barrel_Of_Monkeys	50000	5000000						20	1.781
2020-06-03T05:27:41	Keysarecool	HPLaptop	50000	5000000						3	0.267
2020-06-22T00:24:21	Summy	CHB	50000	5000000						3	0.267
2020-07-02T03:16:27	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.267
2020-07-11T14:00:39	nokno	leo003	50000	5000000						3	0.267
2020-07-14T13:52:31	GAN	OSB-01	50000	5000000	7360979153870570619367	72.640	1	2	878769911981418	1	0.089

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	8B98ABB815617228	0.162
2018-05-18T09:32:45	kkmrkkblmbrbk	old	8B98ABB815617228	0.162

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

8B98ABB815617228

0.162

2018-05-18T09:32:45

kkmrkkblmbrbk

old

8B98ABB815617228

0.162

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 = 3102822, B2 = 43439508 (P-1 stage 2)

B1 = 3102822 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (P-1 stage 2)

B1 = 95000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

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