M2936741 Mersenne number exponent details

Residue

Status

L-L

DF5D74496DEDC545

double-checked

PRP

F29BA9586350E218

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.2963	67.6471%	1000000	20000000	0.2512	5.5409%	20.5474	69.4397%	1.7926%
PrimeNet	2⁵⁹	0.0261	62.7119%	13000	260000	0.0033	3.0712%	0.0294	63.8570%	1.1452%
GPU72	2⁶³	0.5435	65.0794%	17000	300000	0.0040	1.9460%	0.5475	65.7589%	0.6795%
Difference	+5	+19.7528	+2.5677%	+983000	+19700000	+0.2472	+3.5949%	+20.0000	+3.6808%	+3.6808%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.2963

67.6471%

1000000

20000000

0.2512

5.5409%

20.5474

69.4397%

1.7926%

PrimeNet

2⁵⁹

0.0261

62.7119%

13000

260000

0.0033

3.0712%

0.0294

63.8570%

1.1452%

GPU72

2⁶³

0.5435

65.0794%

17000

300000

0.0040

1.9460%

0.5475

65.7589%

0.6795%

Difference

+19.7528

+2.5677%

+983000

+19700000

+0.2472

+3.5949%

+20.0000

+3.6808%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2936741	3883192413988349459633	22	71.718	661139748787576 2³ × 82642468598447	2020-11-04	8	82642468598447	311.40	555,670	1,037,836

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2936741

3883192413988349459633

71.718

661139748787576
2³ × 82642468598447

2020-11-04

82642468598447

311.40

555,670

1,037,836

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.246%
2010-11-08T07:28:00	markr	tiny	105000	2283750		-		-	-	0.028	-	-	2.584%
2015-04-29T15:00:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.541%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:24	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13T19:25:00	Sturle Sunde	kinner.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2012-01-01T15:24:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.334	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.669	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.272	-	-
2016-02-23T09:49:06	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.545	-	-
2017-11-24T17:10:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.089	-	-
2018-12-21T08:04:34	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.18	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.166 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	4.166 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.161	31.308%
25	50000	0.105	90.036%
30	250000	0.006	99.356%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		32	3.703
50000	5000000	3883192413988349459633	4	0.463

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-31T18:58:00	Net_Force	Vista64	50000	5000000						3	0.347
2011-04-13T01:35:00	FJCrodericck	CenterServ	50000	5000000						3	0.347
2013-06-21T14:31:00	Bruce	fx6840-21	50000	5000000						3	0.347
2015-12-29T10:39:22	Bruce	Desk10	50000	5000000						3	0.347
2017-06-02T22:24:00	prime_dive	erazer	50000	5000000						3	0.347
2019-09-07T23:58:07	okay1998	lead	50000	5000000						3	0.347
2020-09-06T03:00:35	J.R. Allen	lapacer	50000	5000000						7	0.810
2020-10-10T03:53:07	mnd9	75203b	50000	5000000						7	0.810
2020-11-04T19:44:32	mnd9	75204	50000	5000000	3883192413988349459633	71.718	4	2	1179912940773920	4	0.463

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	DF5D74496DEDC545	0.250
2018-10-09T07:19:34	kkmrkkblmbrbk	old	DF5D74496DEDC545	0.250

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

DF5D74496DEDC545

0.250

2018-10-09T07:19:34

kkmrkkblmbrbk

old

DF5D74496DEDC545

0.250

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (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

10⁰

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