M3371969 Mersenne number exponent details

≡

M3371969

<<<

>>>

is 2 ^3371969 - 1

has 1015064 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	A8A3E6A604D750ED	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	2⁶⁹	35.4057	68.1159%	4000000	150000000	1.8206	8.1396%	37.2262	70.7112%	2.5952%
PrimeNet	2⁶⁰	0.0455	63.3333%	14000	280000	0.0043	2.8430%	0.0499	64.3758%	1.0424%
GPU72	2⁶⁴	1.0556	65.6250%	18000	320000	0.0052	1.7893%	1.0608	66.2401%	0.6151%
Difference	+5	+34.3501	+2.4909%	+3982000	+149680000	+1.8153	+6.3503%	+36.1654	+4.4711%	+4.4711%

Known prime factors (1 factor, 76.3 bits, 0.00226336% 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
3371969	94308139222117652687993	23	76.320	13984134970119484 2² × 1951 × 1791918883921	2021-10-25	1951	1791918883921	6,369.8	14,868	27,769

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T04:55:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.692%
2011-10-17T13:42:00	harlee	P4_2600	60000	930000		-		-	-	0.016	-	-	1.652%
2014-06-24T22:45:00	Jocelyn Larouche	Manual testing	79035	79035		-		-	-	0.012	-	-	0.652%
2014-10-12T23:58:00	Jocelyn Larouche	Manual testing	98070	98070		-		-	-	0.015	-	-	0.745%
2015-07-27T23:30:00	Squeeky_Squirrel	P4_2600	165000	4331250		-		-	-	0.060	-	-	2.954%
2017-04-13T02:08:48	Jocelyn Larouche	low 4M	330000	3300000	6	-		-	-	0.075	-	-	3.082%
2021-02-14T12:05:39	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.140%
2022-02-25T17:22:07	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.030	-	-	1.113%
2022-04-09T09:24:06	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.152	-	-	2.303%
2022-04-10T15:21:18	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.977%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:27	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.046	-	-
2009-03-27T06:57:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-08-19T06:37:00	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		-	-	2.216	-	-
2017-03-07T14:12:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.432	-	-
2018-11-05T15:44:27	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.865	-	-
2021-08-01T20:43:12	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	17.73	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.190 GHz-days
Estimated T-Level:	2.700

Digits	B1	Curves	Complete	FacMiss
20	11000	54 / 100	0.540	58.117%
25	50000	54 / 280	0.193	82.432%

New Calculation Method

Total ECM effort:	8.190 GHz-days
Estimated T-Level:	2.700

Digits	B1	Complete	FacMiss
20	11000	1.782	16.835%
25	50000	0.160	85.179%
30	250000	0.010	99.016%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4800000		7	1.006
50000	5000000		29	4.244
50000	5000000	94308139222117652687993	4	0.585
50000	6500000		7	1.163
50000	6800000		7	1.191

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-10T07:04:00	sasaki3	ssk_saver	50000	5000000						3	0.439
2011-12-08T15:26:00	S00030	op9020-usff	50000	5000000						3	0.439
2014-10-05T13:22:00	bunddog	debian	50000	5000000						3	0.439
2016-11-05T17:41:38	Dennis Schreiber	z400	50000	5000000						3	0.439
2019-04-10T19:12:22	furkell	furkell1	50000	5000000						3	0.439
2021-03-08T06:42:56	GAN	KL-SCH09	50000	5000000						7	1.025
2021-05-19T17:37:25	kutens	rigel	50000	4800000						7	1.006
2021-05-27T18:57:12	C.D.B.	i7-6850K	50000	5000000						7	1.025
2021-06-24T18:58:38	Dylan Delgado	colab	50000	6800000						7	1.191
2021-08-12T09:07:40	kutens	pbs1	50000	6500000						7	1.163
2021-10-25T20:20:13	daveward2005	d12436	50000	5000000	94308139222117652687993	76.320	4	2	2561506407674137	4	0.585

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	A8A3E6A604D750ED	0.354

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-11-02T17:34:51

_p95holder_

TFL16_PRPt11-E_b

94308139222117652687993

87F079A4DDBA79__

2021-11-03T08:28:28

LaurV

Zero818

94308139222117652687993

87F079A4DDBA791A

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 = 98070 (P-1 stage 1)

B1 = 79035 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

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