M2986163 Mersenne number exponent details

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M2986163

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>>>

is 2 ^2986163 - 1

has 898925 decimal digits

takes 0.254 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	B726943D18A8E4FE	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	2⁶⁸	19.9604	67.6471%	3000000	90000000	0.9552	7.8869%	20.9156	70.1987%	2.5516%
PrimeNet	2⁶⁰	0.0514	63.3333%	12000	220000	0.0029	2.5130%	0.0543	64.2548%	0.9214%
GPU72	2⁶⁴	1.1919	65.6250%	13000	200000	0.0029	1.3857%	1.1948	66.1013%	0.4763%
Difference	+4	+18.7684	+2.0221%	+2987000	+89800000	+0.9523	+6.5012%	+19.7208	+4.0974%	+4.0974%

Known prime factors (1 factor, 77.3 bits, 0.00258977% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2986163	190569441336919256469383	24	77.335	31908747335111857 7 × 17² × 89 × 177224543231	2020-09-15	289	177224543231	12,595	1,191.6	2,225.6

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	-	-	0.247%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2010-10-23T18:17:00	markr	tiny	100000	2025000		-		-	-	0.025	-	-	2.495%
2016-06-20T03:57:42	Jocelyn Larouche	Manual testing	198400	4050000	6	-		-	-	0.050	-	-	3.295%
2017-07-10T01:11:32	Jocelyn Larouche	low 4M	396800	3968000	6	-		-	-	0.073	-	-	3.598%
2019-11-08T19:45:54	BigBrother	Winston	3000000	90000000	12	-		-	-	0.955	-	-	7.887%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-27T00:00:00	mhoney	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
1998-03-17T00:00:00	mhoney	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
1999-05-02T00:00:00	cmorton	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2009-02-14T04:41:00	Sturle Sunde	doak.ifi	2⁶⁰	2⁶¹		-	-	0.051	-	-
2011-11-25T16:46:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.103	-	-
2013-01-07T13:51:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.329	-	-
2015-04-11T15:51:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	0.657	-	-
2015-04-11T15:52:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.251	-	-
2016-02-29T09:27:36	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.502	-	-
2017-12-04T21:22:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.005	-	-
2018-12-28T09:55:50	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.01	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.321 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	2.321 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.645	52.458%
25	50000	0.058	94.336%
30	250000	0.004	99.642%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.741
50000	5000000	190569441336919256469383	5	0.580

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-06T03:09:00	Adel El-Atawy	SRVRARC	50000	5000000						3	0.348
2011-05-09T07:03:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.348
2013-08-04T10:45:00	Bruce	fx6840-21	50000	5000000						3	0.348
2016-01-12T08:21:43	Bruce	Desk7	50000	5000000						3	0.348
2017-07-09T19:07:38	Lelikoid	QH	50000	5000000						3	0.348
2020-09-15T15:28:07	mnd9	75204b	50000	5000000	190569441336919256469383	77.335	5	2	3061128477026	5	0.580

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-27T00:00:00	mhoney	v4_computers	B726943D18A8E4FE	0.254
1998-03-17T00:00:00	mhoney	v4_computers	B726943D18A8E4FE	0.254
1999-06-26T00:00:00	cmorton	v4_computers	B726943D18A8E4FE	0.254
2018-10-21T11:21:48	kkmrkkblmbrbk	old	B726943D18A8E4FE	0.254

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-16T15:40:30

Klaus Nordmann

no1

190569441336919256469383

B435398C3A46A299

2020-09-21T19:43:50

Wentao Huang

tp-win

190569441336919256469383

B435398C3A46A299

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 = 3000000, B2 = 90000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 396800, B2 = 3968000 (P-1 stage 2)

B1 = 198400, B2 = 4050000 (P-1 stage 2)

B1 = 396800 (P-1 stage 1)

B1 = 100000, B2 = 2025000 (P-1 stage 2)

B1 = 198400 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-09-21T19:43:50+00:00

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