M4871981 Mersenne number exponent details

≡

M4871981

<<<

>>>

is 2 ^4871981 - 1

has 1466613 decimal digits

takes 0.675 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	893A84C93320AE32	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	2⁷²	196.2926	68.0556%	2915000	110770000	1.7669	6.1403%	198.0595	70.0170%	1.9615%
PrimeNet	2⁶¹	0.0631	62.2951%	22000	450000	0.0091	3.2990%	0.0722	63.5390%	1.2439%
GPU72	2⁶⁵	1.4975	64.6154%	32000	700000	0.0137	2.3717%	1.5112	65.4546%	0.8392%
Difference	+7	+194.7951	+3.4402%	+2883000	+110070000	+1.7532	+3.7686%	+196.5483	+4.5624%	+4.5624%

Known prime factors:
No known factors for M4871981

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-17T07:51:00	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	0.766%
2013-12-20T02:01:00	David Campeau	i5-2500k	420000	10920000		-		-	-	0.199	-	-	3.195%
2013-12-28T03:37:00	David Campeau	i5-2500k	2915000	110770000		-		-	-	1.767	-	-	6.140%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:03	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.063	-	-
2010-04-20T10:02:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.063	-	-
2011-10-09T22:43:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.328	-	-
2016-02-23T16:39:03	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.201	-	-
2015-01-09T11:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.403	-	-
2015-01-09T11:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.767	-	-
2015-07-21T21:29:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.534	-	-
2017-11-05T12:03:39	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	3.068	-	-
2018-05-08T11:46:37	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	6.135	-	-
2018-07-22T12:21:48	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	12.27	-	-
2018-07-22T12:21:48	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	24.54	-	-
2020-12-04T00:54:02	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	49.08	-	-
2020-12-06T19:22:42	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	98.16	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.885 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.885 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.885

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-04-04T13:20:00	StKl	Workstation	50000	5000000						3	0.628
2014-02-12T16:06:00	driveByUpgrades	Build_4	50000	5000000						3	0.628
2017-04-22T08:43:18	S36049	Wolle4	50000	5000000						3	0.628

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	ANONYMOUS	v4_computers	893A84C93320AE32	0.675
1998-08-02T00:00:00	ANONYMOUS	v4_computers	893A84C93320AE32	0.675
2000-03-15T00:00:00	ANONYMOUS	v4_computers	893A84C93320AE32	0.675

PRP results:
No PRP results for M4871981

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 = 2915000, B2 = 110770000 (P-1 stage 2)

B1 = 2915000 (P-1 stage 1)

B1 = 420000, B2 = 10920000 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-12-06T19:22:42+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