M2528651 Mersenne number exponent details

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M2528651

<<<

>>>

is 2 ^2528651 - 1

has 761200 decimal digits

takes 0.175 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	C1399A24174C933F	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	23.5718	67.6471%	3000000	135000000	1.0250	8.2579%	24.5968	70.3187%	2.6717%
PrimeNet	2⁵⁹	0.0304	62.7119%	11000	190000	0.0021	2.6446%	0.0325	63.6980%	0.9861%
GPU72	2⁶³	0.6312	65.0794%	11000	180000	0.0020	1.4348%	0.6332	65.5804%	0.5011%
Difference	+5	+22.9406	+2.5677%	+2989000	+134820000	+1.0230	+6.8231%	+23.9636	+4.7383%	+4.7383%

Known prime factors (1 factor, 75.1 bits, 0.00297019% 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
2528651	40648562979343842755377	23	75.106	8037598501996488 2³ × 3² × 3533 × 31597314613	2020-06-12	3533	31597314613	3,254.0	173.14	323.37

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.236%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	236250		-		-	-	0.003	-	-	0.796%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.264%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.366%
2011-01-06T23:25:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.530%
2011-03-17T05:57:00	James Heinrich	WHS	300000	8000000		-		-	-	0.072	-	-	3.956%
2017-12-16T19:44:43	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	4.045%
2018-06-26T08:45:00	mikr	MSI	3000000	135000000	12	-		-	-	1.025	-	-	8.258%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
1999-04-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-31T07:43:00	Sturle Sunde	gehry.ifi	2⁶⁰	2⁶¹		-	-	0.061	-	-
2012-06-14T07:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.388	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.776	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.478	-	-
2015-11-08T21:03:09	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.955	-	-
2017-08-08T13:42:07	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.910	-	-
2019-04-15T13:43:02	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.82	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.407 GHz-days
Estimated T-Level:	1.850

Digits	B1	Curves	Complete	FacMiss
20	11000	37 / 100	0.370	68.945%
25	50000	37 / 280	0.132	87.601%

New Calculation Method

Total ECM effort:	3.407 GHz-days
Estimated T-Level:	1.850

Digits	B1	Complete	FacMiss
20	11000	1.194	30.314%
25	50000	0.108	89.774%
30	250000	0.007	99.338%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	3.315
50000	5000000	40648562979343842755377	1	0.092

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-22T10:43:00	Sid & Andy	Bo_Peep	50000	5000000						3	0.276
2010-04-23T05:37:00	lindee	tanagra	50000	5000000						3	0.276
2012-09-14T06:42:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.276
2014-03-16T20:32:00	Andy Incline	Office-PC	50000	5000000						3	0.276
2015-08-03T01:20:00	guru	w6	50000	5000000						3	0.276
2016-03-03T15:07:12	arnaud	CHAMOT09	50000	5000000						3	0.276
2016-07-07T19:20:39	Bruce	test	50000	5000000						3	0.276
2017-05-11T07:00:51	Bruce	eleven	50000	5000000						3	0.276
2017-09-24T07:40:14	S36049	Wolle5	50000	5000000						3	0.276
2018-01-30T07:27:51	junha_kawaguchi	intel_NUC	50000	5000000						3	0.276
2018-10-17T09:13:49	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2020-05-25T02:45:55	mnd9	75203b	50000	5000000						3	0.276
2020-06-12T08:34:03	MarkS	desktop-i7	50000	5000000	40648562979343842755377	75.106	1	2	309555475080518	1	0.092

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	C1399A24174C933F	0.175
1999-04-13T00:00:00	ANONYMOUS	v4_computers	C1399A24174C933F	0.175
2018-06-07T12:47:20	kkmrkkblmbrbk	old	C1399A24174C933F	0.175

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-06-13T16:33:04

CrypticClue

cruncher

40648562979343842755377

4B4D4A6851E9F7B2

2020-06-13T17:08:27

ATH

ec2-PRPCFDC

40648562979343842755377

4B4D4A6851E9F7B2

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 = 135000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 236250 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

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

10¹¹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-06-13T17:08:27+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