M3104501 Mersenne number exponent details

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M3104501

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>>>

is 2 ^3104501 - 1

has 934548 decimal digits

takes 0.264 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	5E50980B78347194	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	19.1995	67.6471%	3104501	637437570	4.6482	10.3961%	23.8477	71.0105%	3.3635%
PrimeNet	2⁶⁰	0.0495	63.3333%	13000	240000	0.0031	2.6429%	0.0526	64.3024%	0.9691%
GPU72	2⁶⁴	1.1465	65.6250%	14000	240000	0.0032	1.5075%	1.1498	66.1432%	0.5182%
Difference	+4	+18.0530	+2.0221%	+3090501	+637197570	+4.6450	+8.8886%	+22.6980	+4.8673%	+4.8673%

Known prime factors (1 factor, 68.3 bits, 0.00219868% 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
3104501	352928927337677030047	21	68.258	56841490361523 3 × 7 × 1051 × 2575392613	2020-12-09	1051	2575392613	21.213	17.316	32.342

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	-	-	0.250%
2009-07-03T07:23:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.762%
2011-08-21T21:41:00	Squeeky_Squirrel	T7500_2200	100000	2125000		-		-	-	0.026	-	-	2.538%
2016-08-27T01:34:29	Jocelyn Larouche	low4M	100000	4250000	6	-		-	-	0.040	-	-	2.960%
2016-12-28T01:45:55	Jocelyn Larouche	low 4M	120000	120000		-		-	-	0.015	-	-	0.951%
2017-01-19T17:19:11	Jocelyn Larouche	low 4M	156000	156000		-		-	-	0.019	-	-	1.099%
2017-02-04T18:42:39	Jocelyn Larouche	low 4M	187200	187200		-		-	-	0.023	-	-	1.210%
2017-02-16T04:19:48	Jocelyn Larouche	low 4M	224640	2246400	6	-		-	-	0.041	-	-	2.939%
2017-03-11T20:20:05	Jocelyn Larouche	low 4M	269568	2695680	6	-		-	-	0.050	-	-	3.149%
2018-07-22T02:27:53	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.049%
2021-01-17T00:34:24	Jocelyn Larouche	Manual testing	310450	3104501	6	-		-	-	0.057	-	-	3.316%
2021-06-17T15:57:28	Jocelyn Larouche	Manual testing	3104501	3104501		-		-	-	0.383	-	-	3.754%
2021-12-19T09:29:23	Jocelyn Larouche	Manual testing	3104501	108997350		-		-	-	1.095	-	-	8.177%
2021-12-22T12:52:22	Jocelyn Larouche	Manual testing	3104501	637437570		-		-	-	4.648	-	-	10.396%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-02-12T17:22:00	Sturle Sunde	ghirardelli.ifi	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-01T06:26:00	markr	Manual testing	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.316	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.632	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.204	-	-
2015-06-11T22:04:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.407	-	-
2017-04-11T13:39:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.814	-	-
2019-02-04T14:28:20	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.63	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.804 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.804 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.774	46.108%
25	50000	0.070	93.242%
30	250000	0.004	99.570%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	2.570
50000	5000000	352928927337677030047	2	0.234

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-30T21:05:00	Aca Arsov	backo6400	50000	5000000						3	0.350
2011-07-18T15:34:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.350
2013-12-01T10:39:00	Bruce	fx6840-21	50000	5000000						3	0.350
2016-05-15T20:09:46	f0rteOC	Mezzo2	50000	5000000						3	0.350
2017-11-07T23:59:17	Volki		50000	5000000						3	0.350
2020-11-01T20:41:09	daveward2005	Dave2	50000	5000000						7	0.818
2020-12-09T01:35:11	GAN	KL-SCH09	50000	5000000	352928927337677030047	68.258	2	2	3736596445116858	2	0.234

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	33A3C7E555F628__	0.264

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-12-09T19:47:41

Jayder

Black_Adder

352928927337677030047

5E50980B78347194

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 = 3104501, B2 = 637437570 (P-1 stage 2)

B1 = 3104501, B2 = 108997350 (P-1 stage 2)

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3104501 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 310450, B2 = 3104501 (P-1 stage 2)

B1 = 269568, B2 = 2695680 (P-1 stage 2)

B1 = 224640, B2 = 2246400 (P-1 stage 2)

B1 = 100000, B2 = 4250000 (P-1 stage 2)

B1 = 310450 (P-1 stage 1)

B1 = 269568 (P-1 stage 1)

B1 = 224640 (P-1 stage 1)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 187200 (P-1 stage 1)

B1 = 156000 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 100000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-12-22T12:52:22+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