M3371399 Mersenne number exponent details

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M3371399

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is 2 ^3371399 - 1

has 1014893 decimal digits

takes 0.354 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	-unknown-	-unknown-
PRP	6FDDC35CB5CEC902	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	2⁷⁰	70.8758	68.5714%	4000000	150000000	1.8206	7.5151%	72.6964	70.9333%	2.3619%
PrimeNet	2⁶⁰	0.0456	63.3333%	14000	280000	0.0043	2.8429%	0.0499	64.3757%	1.0424%
GPU72	2⁶⁴	1.0557	65.6250%	18000	320000	0.0052	1.7892%	1.0610	66.2400%	0.6150%
Difference	+6	+69.8201	+2.9464%	+3982000	+149680000	+1.8153	+5.7259%	+71.6354	+4.6933%	+4.6933%

Known prime factors (1 factor, 75.1 bits, 0.00222816% 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
3371399	41057462516013540898783	23	75.120	6089083866373209 3 × 13 × 41 × 43 × 88559475637	2021-08-17	43	88559475637	2,274.1	734.80	1,372.4

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T04:54:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.590%
2011-10-17T09:22:00	harlee	P4_2600	60000	930000		-		-	-	0.016	-	-	1.449%
2014-06-24T22:45:00	Jocelyn Larouche	Manual testing	79038	79038		-		-	-	0.012	-	-	0.562%
2014-10-12T23:58:00	Jocelyn Larouche	Manual testing	98076	98076		-		-	-	0.015	-	-	0.645%
2015-07-27T10:40:00	Squeeky_Squirrel	P4_2600	165000	4331250		-		-	-	0.060	-	-	2.640%
2017-04-13T02:08:48	Jocelyn Larouche	low 4M	330000	3300000	6	-		-	-	0.075	-	-	2.769%
2021-02-09T04:25:45	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	7.515%
2022-02-25T17:22:08	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.030	-	-	0.975%
2022-04-09T09:24:05	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.152	-	-	2.062%
2022-04-10T15:21:18	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.392%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:26	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.046	-	-
2009-03-27T06:57:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-08-19T21:04:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.091	-	-
2012-11-15T00:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.473	-	-
2016-02-23T16:29:27	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.291	-	-
2015-02-15T12:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.582	-	-
2015-02-15T12:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.108	-	-
2015-03-30T10:38:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.217	-	-
2017-03-07T14:12:53	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.433	-	-
2018-11-05T15:44:27	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.866	-	-
2021-08-01T20:43:11	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	17.73	-	-
2021-08-21T01:11:25	MadPoo	Manual testing	2⁶⁹	2⁷⁰		-	-	35.46	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.504 GHz-days
Estimated T-Level:	2.450

Digits	B1	Curves	Complete	FacMiss
20	11000	49 / 100	0.490	61.112%
25	50000	49 / 280	0.175	83.919%

New Calculation Method

Total ECM effort:	7.504 GHz-days
Estimated T-Level:	2.450

Digits	B1	Complete	FacMiss
20	11000	1.629	19.612%
25	50000	0.146	86.386%
30	250000	0.009	99.101%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	4.244
50000	5000000	41057462516013540898783	6	0.878
50000	6800000		14	2.381

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-14T21:56:00	Matt	Dell	50000	5000000						3	0.439
2011-12-09T07:49:00	Smurgs	Praca	50000	5000000						3	0.439
2014-10-15T14:16:00	S36049	Wolle6	50000	5000000						3	0.439
2016-11-09T16:42:23	Richard Kint	Desktop	50000	5000000						3	0.439
2019-04-10T23:08:20	Idgo	Pentium_Desktop	50000	5000000						3	0.439
2021-02-23T10:36:00	lycorn	colab_A_1	50000	6800000						7	1.191
2021-03-29T16:56:32	Zenzoma	AMD3970X	50000	5000000						7	1.024
2021-05-22T09:44:31	RIHATEC	i7-3770K	50000	5000000						7	1.024
2021-06-27T23:58:17	kutens	canopus	50000	6800000						7	1.191
2021-08-17T02:45:52	daveward2005	Dave2	50000	5000000	41057462516013540898783	75.120	6	2	6856503819662511	6	0.878

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	11A773209ACD9E__	0.354

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-17T05:33:02

GURA LOVE

41057462516013540898783

6FDDC35CB5CEC902

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 126668850 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 330000, B2 = 3300000 (P-1 stage 2)

B1 = 165000, B2 = 4331250 (P-1 stage 2)

B1 = 330000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 165000 (P-1 stage 1)

B1 = 60000, B2 = 930000 (P-1 stage 2)

B1 = 98076 (P-1 stage 1)

B1 = 79038 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T15:21:18+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