M3182521 Mersenne number exponent details

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M3182521

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>>>

is 2 ^3182521 - 1

has 958035 decimal digits

takes 0.271 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	8EA559A8D810FDCD	double-checked
PRP	09784A6AA8F058FC	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	18.7288	67.6471%	3000000	120000000	1.1569	8.2971%	19.8857	70.3314%	2.6844%
PrimeNet	2⁶⁰	0.0483	63.3333%	13000	240000	0.0031	2.6548%	0.0514	64.3068%	0.9734%
GPU72	2⁶⁴	1.1184	65.6250%	15000	260000	0.0035	1.5831%	1.1219	66.1692%	0.5442%
Difference	+4	+17.6104	+2.0221%	+2985000	+119740000	+1.1534	+6.7140%	+18.7638	+4.1622%	+4.1622%

Known prime factors (1 factor, 73.0 bits, 0.00229525% 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
3182521	9756218299660914438439	22	73.047	1532781448992939 3 × 4395067 × 116250139	2021-01-15	4395067	116250139	840.32	1.2945	1.4599

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.252%
2009-07-03T00:58:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.782%
2011-09-12T11:15:00	Squeeky_Squirrel	T7500_2200	60000	975000		-		-	-	0.014	-	-	1.885%
2014-06-01T23:28:00	Jocelyn Larouche	Manual testing	80168	80168		-		-	-	0.010	-	-	0.753%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	100336	100336		-		-	-	0.012	-	-	0.862%
2015-11-24T02:52:51	Jocelyn Larouche	Manual testing	448962	448962		-		-	-	0.055	-	-	1.840%
2015-11-30T00:35:47	Jocelyn Larouche	Manual testing	493858	493858		-		-	-	0.061	-	-	1.918%
2015-12-02T01:07:31	Jocelyn Larouche	Manual testing	543243	543243		-		-	-	0.067	-	-	1.997%
2016-03-18T01:39:29	Jocelyn Larouche	Manual testing	651891	11734038	6	-		-	-	0.155	-	-	4.835%
2019-09-22T08:31:10	mikr	MSI	3000000	120000000	12	-		-	-	1.157	-	-	8.297%
2022-02-27T01:57:30	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	7.626%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.024	-	-
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.024	-	-
2001-07-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-09T16:13:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-17T04:01:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.097	-	-
2013-01-03T08:45:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.308	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.617	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.174	-	-
2015-06-18T20:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.348	-	-
2017-04-26T13:17:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.696	-	-
2019-01-07T14:44:19	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.392	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.483 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	3.483 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	1.095	33.454%
25	50000	0.101	90.415%
30	250000	0.006	99.368%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		3	0.197
50000	5000000		22	2.582
50000	5000000	9756218299660914438439	6	0.704

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-16T14:44:00	willreid	jing	50000	5000000						3	0.352
2011-08-20T18:01:00	sannerud.com	Jim2010	50000	5000000						3	0.352
2014-04-11T07:38:00	S36049	Wolle6	50000	5000000						3	0.352
2016-07-09T08:28:44	Bruce	desk	50000	5000000						3	0.352
2018-04-26T16:06:26	Keldor		50000	50000						3	0.197
2018-12-16T13:26:31	IanGlencross	glenx24	50000	5000000						3	0.352
2020-12-14T08:20:04	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.821
2021-01-15T08:19:40	Zenzoma	AMD3970X	50000	5000000	9756218299660914438439	73.047	6	2	7945268158604989	6	0.704

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-20T00:00:00	ANONYMOUS	v4_computers	8EA559A8D810FDCD	0.271
1998-11-21T00:00:00	ANONYMOUS	v4_computers	8EA559A8D810FDCD	0.271
1999-10-15T00:00:00	ANONYMOUS	v4_computers	8EA559A8D810FDCD	0.271

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-16T12:13:15

seatsea

9756218299660914438439

09784A6AA8F058FC

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 = 120000000 (P-1 stage 2)

B1 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 651891, B2 = 11734038 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 651891 (P-1 stage 1)

B1 = 543243 (P-1 stage 1)

B1 = 493858 (P-1 stage 1)

B1 = 448962 (P-1 stage 1)

B1 = 60000, B2 = 975000 (P-1 stage 2)

B1 = 100336 (P-1 stage 1)

B1 = 80168 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-27T01:57:30+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