M3114109 Mersenne number exponent details

≡

M3114109

<<<

>>>

is 2 ^3114109 - 1

has 937441 decimal digits

takes 0.265 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

1 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	A1AC53F8BEEC15__	unverified 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	19.1403	67.6471%	3000000	100000000	1.0224	8.0515%	20.1627	70.2519%	2.6049%
PrimeNet	2⁶⁰	0.0493	63.3333%	13000	240000	0.0031	2.6444%	0.0525	64.3029%	0.9696%
GPU72	2⁶⁴	1.1430	65.6250%	14000	240000	0.0032	1.5085%	1.1462	66.1435%	0.5185%
Difference	+4	+17.9973	+2.0221%	+2986000	+99760000	+1.0192	+6.5430%	+19.0165	+4.1084%	+4.1084%

Known prime factors (1 factor, 71.6 bits, 0.00230016% 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
3114109	3653037760714808513977	22	71.630	586530169739532 2² × 3² × 10663 × 1527947549	2020-09-24	10663	1527947549	261.62	10.275	19.188

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%
2009-07-03T00:37:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.763%
2011-08-25T03:28:00	Squeeky_Squirrel	T7500_2200	105000	2126250		-		-	-	0.027	-	-	2.564%
2016-09-28T13:16:42	Squeeky_Squirrel	i5-5250U_1600	195000	5508750	12	-		-	-	0.060	-	-	3.530%
2016-10-03T01:22:51	Jocelyn Larouche	low 4M	105000	2551500	6	-		-	-	0.029	-	-	2.675%
2018-07-15T19:00:19	Jocelyn Larouche	low 4M	830000	2490000	6	-		-	-	0.114	-	-	3.416%
2018-07-16T10:16:51	Jocelyn Larouche	low 4M	830000	3320000	6	-		-	-	0.119	-	-	3.695%
2018-09-27T19:39:11	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.051%
2021-01-16T21:12:24	Jocelyn Larouche	Manual testing	860000	3114109	6	-		-	-	0.121	-	-	3.640%
2022-01-06T11:33:55	Jocelyn Larouche	Manual testing	1000000	116447100		-		-	-	0.900	-	-	7.453%

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	-	-
2009-04-14T15:24:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-22T15:25:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.315	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.630	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.200	-	-
2015-06-11T22:04:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.400	-	-
2021-01-16T21:12:24	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.400	-	-
2021-02-18T11:47:34	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.799	-	-
2017-04-14T16:24:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.799	-	-
2019-01-28T14:25:43	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.60	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.857 GHz-days
Estimated T-Level:	1.650

Digits	B1	Curves	Complete	FacMiss
20	11000	33 / 100	0.330	71.773%
25	50000	33 / 280	0.118	88.864%

New Calculation Method

Total ECM effort:	3.857 GHz-days
Estimated T-Level:	1.650

Digits	B1	Complete	FacMiss
20	11000	1.065	34.489%
25	50000	0.096	90.827%
30	250000	0.006	99.409%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		25	2.922
50000	5000000	3653037760714808513977	8	0.935

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-29T17:15:00	unconnected	E5410	50000	5000000						3	0.351
2011-07-24T18:05:00	Pool Party	desk_2	50000	5000000						3	0.351
2013-12-09T13:50:00	Bruce	fx6840-21	50000	5000000						3	0.351
2016-05-20T15:54:36	Richard Kint	xps	50000	5000000						3	0.351
2017-11-19T17:46:44	Thbess		50000	5000000						3	0.351
2020-09-24T02:37:36	mnd9	50869	50000	5000000	3653037760714808513977	71.630	8	2	5415765288764192	8	0.935
2020-09-24T09:06:34	mnd9	50869	50000	5000000						10	1.169

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	5A8EC7A713E267__	0.265

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-26T20:14:17

Klaus Nordmann

no1

3653037760714808513977

A1AC53F8BEEC15__

2020-11-11T15:47:43

Oliver Kruse

IOS-5

3653037760714808513977

A1AC53F8BEEC156F

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 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 116447100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 860000, B2 = 3114109 (P-1 stage 2)

B1 = 830000, B2 = 3320000 (P-1 stage 2)

B1 = 830000, B2 = 2490000 (P-1 stage 2)

B1 = 860000 (P-1 stage 1)

B1 = 830000 (P-1 stage 1)

B1 = 195000, B2 = 5508750 (P-1 stage 2)

B1 = 105000, B2 = 2551500 (P-1 stage 2)

B1 = 105000, B2 = 2126250 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 105000 (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: 2022-01-06T11:33:55+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