M3014237 Mersenne number exponent details

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M3014237

<<<

>>>

is 2 ^3014237 - 1

has 907376 decimal digits

takes 0.257 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	B9343BBFB6848954	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	2⁷⁰	79.2740	68.5714%	32728979	1865551803	16.3626	11.8757%	95.6366	72.3038%	3.7324%
PrimeNet	2⁶⁰	0.0510	63.3333%	12000	220000	0.0029	2.5173%	0.0538	64.2563%	0.9230%
GPU72	2⁶⁴	1.1808	65.6250%	13000	220000	0.0030	1.4276%	1.1838	66.1157%	0.4907%
Difference	+6	+78.0932	+2.9464%	+32715979	+1865331803	+16.3596	+10.4481%	+94.4528	+6.1881%	+6.1881%

Known prime factors (1 factor, 90.9 bits, 0.00301644% 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
3014237	2346601558306337520641110729	28	90.923	389252994755611041972 2² × 3² × 7 × 1544654741093694611	2021-12-29	9	1544654741093694611	148,223,048	1.039e+10	1.940e+10

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.099%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.161%
2010-10-17T22:52:00	markr	tiny	115000	2357500		-		-	-	0.029	-	-	2.099%
2015-07-30T03:08:00	Squeeky_Squirrel	P4_2600	150000	3675000		-		-	-	0.042	-	-	2.458%
2016-08-08T23:06:13	trebor		2000000	2000000		-		-	-	0.247	-	-	2.641%
2016-08-18T13:21:31	trebor		2250000	2250000		-		-	-	0.278	-	-	2.753%
2016-08-20T20:42:34	trebor		2500000	2500000		-		-	-	0.309	-	-	2.856%
2016-08-23T01:01:33	trebor		2750000	2750000		-		-	-	0.339	-	-	2.951%
2016-08-24T23:46:34	trebor		3000000	3000000		-		-	-	0.370	-	-	3.039%
2019-05-28T07:16:17	oodaira	com5	32728979	1865551803	12	-		-	-	16.36	-	-	11.876%
2022-01-26T04:01:32	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	6.262%

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		-	-	0.051	-	-
2009-01-28T08:26:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.051	-	-
2010-09-12T04:47:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.102	-	-
2013-01-07T13:52:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.326	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.651	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.240	-	-
2015-06-01T12:17:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.479	-	-
2017-02-06T12:13:41	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	4.958	-	-
2022-01-19T23:21:42	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.92	-	-
2018-07-16T08:59:43	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.92	-	-
2021-04-08T17:12:20	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.83	-	-
2022-01-18T20:40:07	mikr	Manual testing	2⁶⁹	2⁷⁰		-	-	39.67	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.415 GHz-days
Estimated T-Level:	4.050

Digits	B1	Curves	Complete	FacMiss
20	11000	81 / 100	0.810	44.305%
25	50000	81 / 280	0.289	74.841%

New Calculation Method

Total ECM effort:	9.415 GHz-days
Estimated T-Level:	4.050

Digits	B1	Complete	FacMiss
20	11000	2.613	7.332%
25	50000	0.236	78.966%
30	250000	0.015	98.556%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		78	9.066
50000	5000000	2346601558306337520641110729	3	0.349

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-05T03:11:00	James Hintz	13_060209	50000	5000000						3	0.349
2011-10-17T18:09:00	Pool Party	desk_2	50000	5000000						3	0.349
2013-09-12T10:01:00	Bruce	fx6840-21	50000	5000000						3	0.349
2016-01-19T18:43:16	Bruce	Desk10	50000	5000000						3	0.349
2017-08-03T21:45:39	bayanne	iMac	50000	5000000						3	0.349
2020-09-17T09:41:33	daveward2005	Dave2	50000	5000000						7	0.814
2020-10-17T16:32:55	MarkS	desktop-i7	50000	5000000						7	0.814
2020-11-19T19:19:27	mnd9	27016b	50000	5000000						7	0.814
2020-12-27T08:50:04	daveward2005	Dave2	50000	5000000						7	0.814
2021-01-28T05:54:31	daveward2005	Dave2	50000	5000000						7	0.814
2021-02-26T05:25:30	IanGlencross	glenx24	50000	5000000						7	0.814
2021-04-01T21:38:37	daveward2005	Dave2	50000	5000000						7	0.814
2021-05-24T11:50:41	GAN	KL-SCH04	50000	5000000						7	0.814
2021-12-29T19:34:23	daveward2005	d12436	50000	5000000						7	0.814
2021-12-29T20:07:32	daveward2005	d12436	50000	5000000	2346601558306337520641110729	90.923	3	2	5386811940442306	3	0.349

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	3F6E59C5739B03__	0.257

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-12-31T07:45:40

GURA LOVE

2346601558306337520641110729

B9343BBFB6848954

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 = 32728979, B2 = 1865551803 (P-1 stage 2)

B1 = 32728979 (P-1 stage 1)

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

B1 = 3000000 (P-1 stage 1)

B1 = 2750000 (P-1 stage 1)

B1 = 2500000 (P-1 stage 1)

B1 = 2250000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 150000, B2 = 3675000 (P-1 stage 2)

B1 = 115000, B2 = 2357500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

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TF factor-bounds graph:

2⁷⁰

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2¹⁰⁰

Last modified: 2022-01-26T04:01:32+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