M3568993 Mersenne number exponent details

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M3568993

<<<

>>>

is 2 ^3568993 - 1

has 1074374 decimal digits

takes 0.375 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	B23DAE5BF2D62AF5	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	2⁶⁸	16.7008	67.6471%	1000000	130318650	1.2253	7.6853%	17.9260	70.1335%	2.4864%
PrimeNet	2⁶⁰	0.0430	63.3333%	15000	300000	0.0046	2.9706%	0.0477	64.4226%	1.0892%
GPU72	2⁶⁴	0.9973	65.6250%	20000	400000	0.0062	1.9773%	1.0035	66.3047%	0.6797%
Difference	+4	+15.7035	+2.0221%	+980000	+129918650	+1.2191	+5.7080%	+16.9225	+3.8288%	+3.8288%

Known prime factors (1 factor, 71.2 bits, 0.00199383% 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
3568993	2637250692391618935607	22	71.160	369467058690171 3³ × 13 × 1052612702821	2019-11-12	27	1052612702821	229.41	8,733.7	16,312

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-05-17T00:00:00	ANONYMOUS	v4_computers	15000	187500		-		-	-	0.004	-	-	0.795%
2010-09-13T05:21:00	markr	tiny	100000	2225000		-		-	-	0.033	-	-	2.621%
2016-10-06T15:59:26	Squeeky_Squirrel	P4_2600	225000	6525000	12	-		-	-	0.087	-	-	3.807%
2016-12-28T01:45:59	Jocelyn Larouche	low 4M	20000	20000		-		-	-	0.003	-	-	0.286%
2016-12-29T20:13:40	Jocelyn Larouche	low 4M	80000	80000		-		-	-	0.012	-	-	0.769%
2017-01-04T22:58:45	Jocelyn Larouche	low 4M	120000	120000		-		-	-	0.018	-	-	0.975%
2022-04-08T06:41:02	Jocelyn Larouche	Manual testing	1000000	130318650		-		-	-	1.225	-	-	7.685%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.043	-	-
2009-03-15T19:18:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.043	-	-
2011-06-17T23:43:00	markr	Manual testing	2¹	2⁶²		-	-	0.172	-	-
2012-07-02T04:03:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.447	-	-
2016-02-23T16:29:33	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.275	-	-
2015-01-30T19:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.550	-	-
2015-01-30T19:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.047	-	-
2016-03-02T09:22:01	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.094	-	-
2017-01-20T05:22:15	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.188	-	-
2018-12-10T15:07:46	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.375	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.072 GHz-days
Estimated T-Level:	0.700

Digits	B1	Curves	Complete	FacMiss
20	11000	14 / 100	0.140	86.875%
25	50000	14 / 280	0.050	95.114%

New Calculation Method

Total ECM effort:	2.072 GHz-days
Estimated T-Level:	0.700

Digits	B1	Complete	FacMiss
20	11000	0.452	63.660%
25	50000	0.041	96.001%
30	250000	0.003	99.749%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.776
50000	5000000	2637250692391618935607	2	0.296

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-09T20:05:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.444
2012-04-15T23:50:00	oodaira	Linux01	50000	5000000						3	0.444
2015-06-26T15:40:00	Bruce	desk16	50000	5000000						3	0.444
2017-03-21T00:04:08	deo2016	deo2016.home2	50000	5000000						3	0.444
2019-11-12T23:18:04	mnd9	25836b	50000	5000000	2637250692391618935607	71.160	2	2	281617355855037	2	0.296

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-03T00:00:00	ANONYMOUS	v4_computers	B23DAE5BF2D62AF5	0.375
2000-06-23T00:00:00	ANONYMOUS	v4_computers	B23DAE5BF2D62AF5	0.375
2000-06-29T00:00:00	ANONYMOUS	v4_computers	036B718475B12F__	0.375

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-11-13T13:49:55

Niels_Mache_Nextcloud

SuperDry-X

2637250692391618935607

5C6A4071C8EF1CAD

2019-11-13T14:20:41

ATH

ec2-PRPCFDC

2637250692391618935607

5C6A4071C8EF1CAD

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 = 1000000, B2 = 130318650 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 225000, B2 = 6525000 (P-1 stage 2)

B1 = 225000 (P-1 stage 1)

B1 = 100000, B2 = 2225000 (P-1 stage 2)

B1 = 120000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 80000 (P-1 stage 1)

B1 = 15000, B2 = 187500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-08T06:41:02+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