M3122869 Mersenne number exponent details

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M3122869

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is 2 ^3122869 - 1

has 940078 decimal digits

takes 0.266 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	7BCDD17A191F2034	double-checked
PRP	44C230AB9D613C09	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	19.0866	67.6471%	3000000	100000000	1.0224	8.0537%	20.1090	70.2527%	2.6056%
PrimeNet	2⁶⁰	0.0492	63.3333%	13000	240000	0.0031	2.6457%	0.0523	64.3034%	0.9701%
GPU72	2⁶⁴	1.1398	65.6250%	15000	240000	0.0034	1.5416%	1.1431	66.1549%	0.5299%
Difference	+4	+17.9468	+2.0221%	+2985000	+99760000	+1.0191	+6.5121%	+18.9659	+4.0977%	+4.0977%

Known prime factors (1 factor, 71.0 bits, 0.00227449% 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
3122869	2409946995919915968457	22	71.029	385854641344212 2² × 3 × 32154553445351	2021-05-01	4	32154553445351	195.25	216,200	403,802

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.251%
2009-07-03T00:45:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.763%
2011-08-28T03:47:00	Squeeky_Squirrel	T7500_2200	105000	2126250		-		-	-	0.027	-	-	2.565%
2016-09-30T08:50:34	Squeeky_Squirrel	i5-5250U_1600	195000	5460000	12	-		-	-	0.059	-	-	3.525%
2018-07-15T19:00:15	Jocelyn Larouche	low 4M	692144	2768576		-		-	-	0.099	-	-	3.479%
2018-07-16T10:16:45	Jocelyn Larouche	low 4M	692144	4152864		-		-	-	0.109	-	-	3.860%
2018-11-24T22:43:04	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.054%
2022-02-20T22:19:22	Jocelyn Larouche	Manual testing	1000000	128282700		-		-	-	0.979	-	-	7.560%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-14T15:46:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-15T21:24:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.098	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.314	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.629	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.196	-	-
2015-06-14T13:51:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.393	-	-
2017-04-14T16:24:31	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.786	-	-
2019-01-14T11:03:54	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.57	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.198 GHz-days
Estimated T-Level:	2.650

Digits	B1	Curves	Complete	FacMiss
20	11000	53 / 100	0.530	58.704%
25	50000	53 / 280	0.189	82.727%

New Calculation Method

Total ECM effort:	6.198 GHz-days
Estimated T-Level:	2.650

Digits	B1	Complete	FacMiss
20	11000	1.710	18.092%
25	50000	0.155	85.683%
30	250000	0.010	99.053%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		50	5.848
50000	5000000	2409946995919915968457	3	0.351

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-26T07:32:00	Tom Bammann	Work	50000	5000000						3	0.351
2011-07-24T16:26:00	Smurgs	Praca	50000	5000000						3	0.351
2013-12-19T22:37:00	Bruce	apandya-DESK11	50000	5000000						3	0.351
2016-05-29T23:57:29	remvad	home	50000	5000000						3	0.351
2017-12-05T23:18:40	AskingNet	AskingNet	50000	5000000						3	0.351
2020-11-12T17:28:34	C.D.B.	i7-6850K	50000	5000000						7	0.819
2020-12-19T19:14:22	Zenzoma	AMD3970X	50000	5000000						7	0.819
2021-01-20T15:10:48	LordJulius	Babybox	50000	5000000						7	0.819
2021-03-21T00:19:13	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.819
2021-04-20T12:29:56	Zenzoma	AMD3970X	50000	5000000						7	0.819
2021-05-01T18:23:15	daveward2005	Dave2	50000	5000000	2409946995919915968457	71.029	3	2	4568086298481893	3	0.351

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-16T00:00:00	oerwin	v4_computers	7BCDD17A191F2034	0.266
1999-11-04T00:00:00	ANONYMOUS	v4_computers	7BCDD17A191F2034	0.266

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-05-02T14:37:13

XZT

N4640G2

2409946995919915968457

44C230AB9D613C09

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 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 128282700 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 692144, B2 = 4152864 (P-1 stage 2)

B1 = 692144, B2 = 2768576 (P-1 stage 2)

B1 = 692144 (P-1 stage 1)

B1 = 195000, B2 = 5460000 (P-1 stage 2)

B1 = 105000, B2 = 2126250 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

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10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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10¹³

10¹⁴

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-20T22:19:22+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