M2106631 Mersenne number exponent details

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M2106631

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>>>

is 2 ^2106631 - 1

has 634160 decimal digits

takes 0.139 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	6F036EAA8CE378A0	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	14.1049	67.1642%	500000	15000000	0.1230	5.1551%	14.2279	68.8569%	1.6927%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6793%	0.0199	63.0853%	1.0163%
GPU72	2⁶²	0.2916	64.5161%	10000	140000	0.0016	1.4522%	0.2933	65.0314%	0.5153%
Difference	+5	+13.8133	+2.6481%	+490000	+14860000	+0.1214	+3.7029%	+13.9347	+3.8255%	+3.8255%

Known prime factors (1 factor, 75.1 bits, 0.00356705% 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
2106631	41758746510437380976351	23	75.144	9911262701070425 5² × 396450508042817	2015-08-02	25	396450508042817	5,994.9	2,059,263	3,846,130

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2009-08-02T01:01:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.021%
2010-12-29T20:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.415%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.596%
2011-01-24T23:41:00	James Heinrich	Q6600	140000	3010000		-		-	-	0.028	-	-	3.100%
2016-03-16T12:13:28	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.155%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T09:12:33	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.073	-	-
2009-01-02T20:25:00	Sturle Sunde	fungo.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-29T23:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2013-09-04T10:21:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.466	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.932	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.774	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.120 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.120 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.790	45.395%
25	50000	0.071	93.105%
30	250000	0.004	99.560%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.277
50000	5000000	41758746510437380976351	2	0.170
50000	6570949		7	0.672

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-14T22:45:00	Chang Chia-Tche	euler06	50000	5000000						3	0.255
2009-11-11T15:25:00	James Hintz	ryan	50000	5000000						3	0.255
2011-06-28T14:19:00	Csaba Vágó	timigep	50000	5000000						3	0.255
2013-04-07T11:28:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-10-27T23:13:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.255
2015-08-02T14:33:00	guru	w6	50000	5000000	41758746510437380976351	75.144	2	2		2	0.170
2022-05-17T21:33:44	debrouxl	dl380g9-1	50000	6570949						7	0.672

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	D578182538E60E__	0.139

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T02:34:49

Oliver Kruse

GTX-1

41758746510437380976351

8552B9B54E70A0__

2017-11-17T08:03:41

kkmrkkblmbrbk

c4.xlarge

41758746510437380976351

8552B9B54E70A0__

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

B1 = 500000 (P-1 stage 1)

B1 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

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10⁰

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10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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10¹²

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TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-17T21:33:44+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