M3072847 Mersenne number exponent details

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M3072847

<<<

>>>

is 2 ^3072847 - 1

has 925020 decimal digits

takes 0.262 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	A666DF489458EA53	double-checked
PRP	D9AC7759D2879397	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	38.8522	68.1159%	3000000	100000000	1.0224	7.4116%	39.8746	70.4791%	2.3631%
PrimeNet	2⁶⁰	0.0500	63.3333%	12000	220000	0.0029	2.5263%	0.0529	64.2596%	0.9263%
GPU72	2⁶⁴	1.1583	65.6250%	14000	220000	0.0031	1.4671%	1.1614	66.1293%	0.5043%
Difference	+5	+37.6939	+2.4909%	+2986000	+99780000	+1.0193	+5.9445%	+38.7132	+4.3497%	+4.3497%

Known prime factors (1 factor, 69.9 bits, 0.00227408% 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
3072847	1085696581139433242129	22	69.879	176659719982712 2³ × 587 × 37619190797	2021-03-30	587	37619190797	50.239	252.94	472.43

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.201%
2010-09-21T08:17:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.372%
2016-10-23T00:36:39	Squeeky_Squirrel	P4_2600	195000	5460000	12	-		-	-	0.059	-	-	3.155%
2017-01-04T22:58:53	Jocelyn Larouche	low 4M	132000	132000		-		-	-	0.016	-	-	0.872%
2018-01-05T13:27:46	Jocelyn Larouche	low 4M	780000	780000		-		-	-	0.096	-	-	2.059%
2018-01-29T11:19:52	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	7.412%
2022-01-25T08:16:02	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	6.852%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
1998-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
2001-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-13T15:42:00	Sturle Sunde	goomba.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-10-27T11:29:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.100	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.319	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.639	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.216	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.432	-	-
2017-05-14T00:43:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.864	-	-
2022-01-19T07:45:03	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.73	-	-
2018-08-05T23:31:44	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.73	-	-
2021-03-23T11:34:14	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.45	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.064 GHz-days
Estimated T-Level:	2.600

Digits	B1	Curves	Complete	FacMiss
20	11000	52 / 100	0.520	59.297%
25	50000	52 / 280	0.186	83.023%

New Calculation Method

Total ECM effort:	6.064 GHz-days
Estimated T-Level:	2.600

Digits	B1	Complete	FacMiss
20	11000	1.677	18.686%
25	50000	0.152	85.933%
30	250000	0.009	99.071%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		50	5.831
50000	5000000	1085696581139433242129	2	0.233

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-14T03:09:00	dragon325	x-home-quad	50000	5000000						3	0.350
2011-06-26T08:31:00	Smurgs	Praca	50000	5000000						3	0.350
2013-11-06T04:05:00	Bruce	fx6840-21	50000	5000000						3	0.350
2016-03-08T08:31:03	Ismo Laitela		50000	5000000						3	0.350
2017-09-29T02:23:12	jafarism	jafarism-r07	50000	5000000						3	0.350
2020-10-22T04:44:34	Nesowa	6700T	50000	5000000						7	0.816
2020-11-17T23:18:41	lycorn	colab_ES_1	50000	5000000						7	0.816
2020-12-24T20:09:28	Dylan Delgado	colab	50000	5000000						7	0.816
2021-02-23T07:15:55	mnd9	75211backdoor	50000	5000000						7	0.816
2021-03-26T23:03:05	mnd9	kitchen	50000	5000000						7	0.816
2021-03-30T11:09:40	GAN	KL-SCH02	50000	5000000	1085696581139433242129	69.879	2	2	3714237795747242	2	0.233

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-13T00:00:00	ANONYMOUS	v4_computers	A666DF489458EA53	0.262
1999-11-17T00:00:00	ANONYMOUS	v4_computers	A666DF489458EA53	0.262

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-03-31T16:17:38

XZT

N4640G1

1085696581139433242129

D9AC7759D2879397

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 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 780000 (P-1 stage 1)

B1 = 195000, B2 = 5460000 (P-1 stage 2)

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

B1 = 195000 (P-1 stage 1)

B1 = 132000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-25T08:16:02+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