M3050693 Mersenne number exponent details

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M3050693

<<<

>>>

is 2 ^3050693 - 1

has 918351 decimal digits

takes 0.260 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	7A267C7858B7604E	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	39.1343	68.1159%	3050693	667691640	4.8454	9.6667%	43.9797	71.1981%	3.0821%
PrimeNet	2⁶⁰	0.0503	63.3333%	12000	220000	0.0029	2.5229%	0.0532	64.2584%	0.9251%
GPU72	2⁶⁴	1.1667	65.6250%	14000	220000	0.0031	1.4650%	1.1698	66.1286%	0.5036%
Difference	+5	+37.9676	+2.4909%	+3036693	+667471640	+4.8423	+8.2017%	+42.8099	+5.0695%	+5.0695%

Known prime factors (1 factor, 101.3 bits, 0.00332198% 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
3050693	3216519015376507736741944800577	31	101.343	527178417391803720784416 2⁵ × 3 × 7² × 109 × 349 × 853 × 1710629 × 2018987	2017-09-26	1710629	2018987	4.744e+10	0.2132	0.4296

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%
2010-10-04T16:13:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.369%
2016-03-16T02:33:05	Squeeky_Squirrel	P4_2600	205000	5688750	12	-		-	-	0.062	-	-	3.207%
2017-09-26T23:42:50	mikr	MSI	3000000	3000000			3216519015376507736741944800577	31	101.343	0.370	0.519	0.740	3.360%
2021-11-20T13:50:21	Jocelyn Larouche	Manual testing	3050693	3050693		-	skipped known factor: 3216519015376507736741944800577	-	-	0.376	-	-	3.378%
2021-12-08T12:48:15	Jocelyn Larouche	Manual testing	3050693	30506930	12	-	skipped known factor: 3216519015376507736741944800577	-	-	0.561	-	-	6.024%
2021-12-21T15:51:57	Jocelyn Larouche	Manual testing	3050693	139258350		-	skipped known factor: 3216519015376507736741944800577	-	-	1.292	-	-	7.807%
2021-12-22T09:19:37	Jocelyn Larouche	Manual testing	3050693	667691640		-	skipped known factor: 3216519015376507736741944800577	-	-	4.845	-	-	9.667%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-12T22:25:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-03-18T17:50:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.322	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.644	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.225	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.450	-	-
2021-01-16T21:12:25	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.450	-	-
2021-02-18T11:47:34	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.899	-	-
2017-05-07T02:13:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.899	-	-
2021-02-25T22:13:20	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.80	-	-
2022-01-09T11:52:12	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.60	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.747 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.747 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.747

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-15T05:33:00	oodaira	Win02	50000	5000000						3	0.349
2011-06-13T10:15:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.349
2013-10-19T21:35:00	Pool Party	St.P.p	50000	5000000						3	0.349
2016-01-31T04:41:22	Bruce	Desk7	50000	5000000						3	0.349
2017-09-06T09:51:10	driveByUpgrades	AMD8	50000	5000000						3	0.349

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	7A267C7858B7604E	0.260

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:10:15

alpertron

Manual testing

3216519015376507736741944800577

FBFD71B05253CA__

2017-11-17T14:23:34

Oliver Kruse

Threadripper

3216519015376507736741944800577

FBFD71B05253CA__

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 = 3050693, B2 = 667691640 (P-1 stage 2)

B1 = 3050693, B2 = 139258350 (P-1 stage 2)

B1 = 3050693, B2 = 30506930 (P-1 stage 2)

B1 = 3050693 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 205000, B2 = 5688750 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2022-01-09T11:52:12+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