M2950093 Mersenne number exponent details

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M2950093

<<<

>>>

is 2 ^2950093 - 1

has 888067 decimal digits

takes 0.251 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	5AEDB3E2BE5E5A11	double-checked
PRP	6B8C3C56B030A18E	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	40.4688	68.1159%	1045446	22000000	0.2699	5.1708%	40.7387	69.7646%	1.6487%
PrimeNet	2⁶⁰	0.0521	63.3333%	12000	220000	0.0029	2.5073%	0.0549	64.2527%	0.9194%
GPU72	2⁶⁴	1.2065	65.6250%	12000	200000	0.0027	1.3466%	1.2093	66.0879%	0.4629%
Difference	+5	+39.2623	+2.4909%	+1033446	+21800000	+0.2672	+3.8241%	+39.5295	+3.6767%	+3.6767%

Known prime factors (1 factor, 86.3 bits, 0.00292523% 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
2950093	95052978891302722284800167	26	86.297	16110166508530870431 3 × 5370055502843623477	2021-08-02	3	5370055502843623477	9,165,262	3.611e+10	6.744e+10

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.199%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.120%
2010-11-03T12:44:00	markr	tiny	95000	1971250		-		-	-	0.024	-	-	2.172%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	116757	116757		-		-	-	0.014	-	-	0.806%
2015-01-26T12:23:00	Jocelyn Larouche	Manual testing	141275	141275		-		-	-	0.017	-	-	0.900%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	188036	188036		-		-	-	0.023	-	-	1.053%
2015-02-02T07:32:00	Jocelyn Larouche	Manual testing	206839	206839		-		-	-	0.026	-	-	1.107%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	366425	366425		-		-	-	0.045	-	-	1.470%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	403067	403067		-		-	-	0.050	-	-	1.537%
2015-02-23T15:50:00	Jocelyn Larouche	Manual testing	443373	443373		-		-	-	0.055	-	-	1.605%
2015-02-27T19:06:00	Jocelyn Larouche	Manual testing	487710	487710		-		-	-	0.060	-	-	1.675%
2015-03-10T07:55:00	Jocelyn Larouche	Manual testing	536481	536481		-		-	-	0.066	-	-	1.747%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	590129	590129		-		-	-	0.073	-	-	1.821%
2015-03-29T20:50:00	Jocelyn Larouche	Manual testing	714055	714055		-		-	-	0.088	-	-	1.973%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	785460	785460		-		-	-	0.097	-	-	2.052%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	950406	950406		-		-	-	0.117	-	-	2.215%
2015-05-02T08:23:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.056%
2016-09-08T02:10:15	Jocelyn Larouche	low4M	1045446	22000000	12	-		-	-	0.270	-	-	5.171%

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		-	-	0.052	-	-
2009-02-14T18:59:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-11-24T05:58:00	markr	Manual testing	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.333	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.666	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.267	-	-
2016-02-25T09:22:06	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.533	-	-
2017-11-28T10:01:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.066	-	-
2018-12-24T00:53:32	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.13	-	-
2021-05-19T10:49:17	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	20.26	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.172 GHz-days
Estimated T-Level:	4.300

Digits	B1	Curves	Complete	FacMiss
20	11000	86 / 100	0.860	42.133%
25	50000	86 / 280	0.307	73.514%

New Calculation Method

Total ECM effort:	10.172 GHz-days
Estimated T-Level:	4.300

Digits	B1	Complete	FacMiss
20	11000	3.346	3.522%
25	50000	0.309	73.381%
30	250000	0.020	98.064%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		74	8.569
50000	6750000		7	0.935
50000	6750000	95052978891302722284800167	5	0.668

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-29T12:45:00	Sturle Sunde	iago.ifi	50000	5000000						3	0.347
2011-04-20T00:04:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.347
2013-07-04T18:01:00	Bruce	E6510	50000	5000000						3	0.347
2016-01-02T01:47:58	Bruce	Desk7	50000	5000000						3	0.347
2017-06-06T07:55:59	Bruce	desk	50000	5000000						3	0.347
2019-10-07T10:57:14	Claude Portenier	Petit-Idiot	50000	5000000						3	0.347
2020-09-14T07:46:38	mnd9	25836b	50000	5000000						7	0.811
2020-10-14T01:04:24	mnd9	75211backdoor	50000	5000000						7	0.811
2020-11-12T22:53:32	lycorn	colab_D_1	50000	5000000						7	0.811
2020-12-19T21:28:06	daveward2005	Dave2	50000	5000000						7	0.811
2021-01-20T13:32:38	LordJulius	Babybox	50000	5000000						7	0.811
2021-02-18T15:45:31	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.811
2021-03-21T00:19:12	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.811
2021-05-07T10:07:58	IanGlencross	glenx24	50000	5000000						7	0.811
2021-06-19T01:41:32	LaurV	butu	50000	6750000						7	0.935
2021-08-02T19:50:35	kutens	ryzen1	50000	6750000	95052978891302722284800167	86.297	5	2	6335737165259340	5	0.668

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	ANONYMOUS	v4_computers	5AEDB3E2BE5E5A11	0.251
2018-10-12T14:52:49	kkmrkkblmbrbk	old	5AEDB3E2BE5E5A11	0.251

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-04T04:02:35

kutens

ryzen2

95052978891302722284800167

6B8C3C56B030A18E

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 = 1045446, B2 = 22000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1045446 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 950406 (P-1 stage 1)

B1 = 785460 (P-1 stage 1)

B1 = 714055 (P-1 stage 1)

B1 = 590129 (P-1 stage 1)

B1 = 536481 (P-1 stage 1)

B1 = 487710 (P-1 stage 1)

B1 = 443373 (P-1 stage 1)

B1 = 403067 (P-1 stage 1)

B1 = 366425 (P-1 stage 1)

B1 = 206839 (P-1 stage 1)

B1 = 95000, B2 = 1971250 (P-1 stage 2)

B1 = 188036 (P-1 stage 1)

B1 = 141275 (P-1 stage 1)

B1 = 116757 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

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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: 2021-08-04T04:02:35+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