M3061111 Mersenne number exponent details

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M3061111

<<<

>>>

is 2 ^3061111 - 1

has 921487 decimal digits

takes 0.261 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	96CD4C8E57DB80CF	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	2⁶⁹	39.0011	68.1159%	32462415	1850357655	16.2293	12.6538%	55.2305	72.1505%	4.0346%
PrimeNet	2⁶⁰	0.0502	63.3333%	12000	220000	0.0029	2.5245%	0.0531	64.2590%	0.9256%
GPU72	2⁶⁴	1.1628	65.6250%	14000	220000	0.0031	1.4660%	1.1659	66.1289%	0.5039%
Difference	+5	+37.8384	+2.4909%	+32448415	+1850137655	+16.2262	+11.1879%	+54.0646	+6.0216%	+6.0216%

Known prime factors (1 factor, 74.8 bits, 0.00244333% 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
3061111	32732560362813578360497	23	74.793	5346516405777768 2³ × 3² × 13 × 23 × 29 × 8563853339	2021-04-10	29	8563853339	1,538.8	57.581	107.55

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	-	-	0.201%
2010-09-25T21:03:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.370%
2016-03-25T12:45:15	Squeeky_Squirrel	P4_2600	205000	5740000	12	-		-	-	0.063	-	-	3.214%
2017-11-17T03:58:27	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	7.409%
2022-02-06T12:04:25	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	6.849%
2022-04-10T05:27:58	oodaira	com5	32462415	1850357655	12	-		-	-	16.23	-	-	12.654%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-13T16:30:00	Sturle Sunde	gimo.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-10-06T23:51:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.100	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.321	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.641	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.221	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.441	-	-
2017-05-09T09:30:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.882	-	-
2022-01-20T22:38:00	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.76	-	-
2018-07-30T10:12:18	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.76	-	-
2021-04-06T16:36:35	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.53	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.536 GHz-days
Estimated T-Level:	2.750

Digits	B1	Curves	Complete	FacMiss
20	11000	55 / 100	0.550	57.535%
25	50000	55 / 280	0.196	82.137%

New Calculation Method

Total ECM effort:	6.536 GHz-days
Estimated T-Level:	2.750

Digits	B1	Complete	FacMiss
20	11000	1.790	16.700%
25	50000	0.162	85.036%
30	250000	0.010	99.006%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		46	5.361
50000	5000000	32732560362813578360497	2	0.233
50000	6750000		7	0.942

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-20T10:33:00	Martti Järvi	Wanda	50000	5000000						3	0.350
2011-06-19T12:06:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.350
2013-10-28T00:31:00	aubie88	mac_mini	50000	5000000						3	0.350
2016-02-15T00:51:20	Dane McRae	Precision	50000	5000000						3	0.350
2016-02-16T15:58:35	Dane McRae	Manual testing	50000	5000000						3	0.350
2020-10-15T00:42:56	Jaytholomew	Jaytholomew	50000	5000000						10	1.165
2020-11-25T19:25:51	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.816
2020-12-31T11:50:53	mnd9	kitchen	50000	5000000						7	0.816
2021-01-31T01:28:06	lycorn	colab_D	50000	6750000						7	0.942
2021-03-09T04:36:05	GAN	KL-SCH02	50000	5000000						7	0.816
2021-04-10T07:57:46	daveward2005	Dave2	50000	5000000	32732560362813578360497	74.793	2	2	924724661796746	2	0.233

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	ANONYMOUS	v4_computers	EA8160FFC908CB__	0.261

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-10T08:36:35

123456789123456789

byebye

32732560362813578360497

96CD4C8E57DB80CF

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 = 32462415, B2 = 1850357655 (P-1 stage 2)

B1 = 32462415 (P-1 stage 1)

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

B1 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 205000, B2 = 5740000 (P-1 stage 2)

B1 = 110000, B2 = 2447500 (P-1 stage 2)

B1 = 205000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T05:27:58+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