M3218261 Mersenne number exponent details

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M3218261

<<<

>>>

is 2 ^3218261 - 1

has 968794 decimal digits

takes 0.274 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	3FCEDA230C33C4B7	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	37.0967	68.1159%	4000000	150000000	1.4753	8.1030%	38.5720	70.6995%	2.5836%
PrimeNet	2⁶⁰	0.0477	63.3333%	13000	240000	0.0031	2.6602%	0.0509	64.3087%	0.9754%
GPU72	2⁶⁴	1.1060	65.6250%	16000	260000	0.0036	1.6175%	1.1096	66.1810%	0.5560%
Difference	+5	+35.9907	+2.4909%	+3984000	+149740000	+1.4717	+6.4855%	+37.4624	+4.5185%	+4.5185%

Known prime factors (1 factor, 76.9 bits, 0.00238980% 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
3218261	141967274908396430089657	24	76.910	22056519795690348 2² × 3³ × 2017 × 101252868193	2021-08-10	2017	101252868193	7,892.7	680.80	1,271.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:42:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.669%
2011-09-25T01:06:00	harlee	P4_2600	60000	1035000		-		-	-	0.014	-	-	1.686%
2014-06-03T02:15:00	Jocelyn Larouche	Manual testing	79944	79944		-		-	-	0.010	-	-	0.651%
2014-09-29T22:05:00	Jocelyn Larouche	Manual testing	99888	99888		-		-	-	0.012	-	-	0.747%
2015-12-14T03:34:38	Squeeky_Squirrel	P4_2600	155000	3952500	6	-		-	-	0.045	-	-	2.844%
2016-05-13T03:13:59	Jocelyn Larouche	Manual testing	351421	6325578	6	-		-	-	0.084	-	-	3.583%
2020-02-22T22:28:08	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.103%
2022-03-11T21:35:40	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	7.002%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-07T22:16:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-20T05:27:00	markr	Manual testing	2¹	2⁶²		-	-	0.191	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.305	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.610	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.161	-	-
2015-06-24T21:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.322	-	-
2017-03-17T19:55:21	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.644	-	-
2019-01-07T14:44:16	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.288	-	-
2021-01-28T21:25:07	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.58	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.173 GHz-days
Estimated T-Level:	3.050

Digits	B1	Curves	Complete	FacMiss
20	11000	61 / 100	0.610	54.169%
25	50000	61 / 280	0.218	80.393%

New Calculation Method

Total ECM effort:	7.173 GHz-days
Estimated T-Level:	3.050

Digits	B1	Complete	FacMiss
20	11000	1.968	13.977%
25	50000	0.178	83.707%
30	250000	0.011	98.911%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	6.702
50000	5000000	141967274908396430089657	4	0.470

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-15T01:53:00	Martti Järvi	Wanda	50000	5000000						3	0.353
2011-09-04T22:10:00	S00030	op9020-usff	50000	5000000						3	0.353
2014-05-10T02:41:00	Bruce	fx6840-21	50000	5000000						3	0.353
2016-08-04T14:54:56	ANONYMOUS	PD925	50000	5000000						3	0.353
2018-09-26T16:14:20	IanGlencross	glenx24	50000	5000000						3	0.353
2020-12-25T15:36:39	tonyw	Worke	50000	5000000						7	0.823
2021-01-25T22:03:45	daveward2005	Dave2	50000	5000000						7	0.823
2021-02-23T08:54:11	Zenzoma	AMD3970X	50000	5000000						7	0.823
2021-03-27T18:32:56	Zenzoma	AMD3970X	50000	5000000						7	0.823
2021-05-20T11:56:01	RIHATEC	i7-3770K	50000	5000000						7	0.823
2021-06-26T08:02:07	daveward2005	Dave2	50000	5000000						7	0.823
2021-08-10T05:23:27	GAN	KL-SCH01	50000	5000000	141967274908396430089657	76.910	4	2		4	0.470

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-05T00:00:00	ANONYMOUS	v4_computers	3FCEDA230C33C4B7	0.274
1999-10-21T00:00:00	ANONYMOUS	v4_computers	3FCEDA230C33C4B7	0.274

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-13T08:56:52

GURA LOVE

141967274908396430089657

977E82C32983F94C

2021-08-13T22:07:38

GAN

LMS-11

141967274908396430089657

977E82C32983F94C

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 = 134343300 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 351421, B2 = 6325578 (P-1 stage 2)

B1 = 155000, B2 = 3952500 (P-1 stage 2)

B1 = 351421 (P-1 stage 1)

B1 = 155000 (P-1 stage 1)

B1 = 60000, B2 = 1035000 (P-1 stage 2)

B1 = 99888 (P-1 stage 1)

B1 = 79944 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (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

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-11T21:35:40+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