M648617 Mersenne number exponent details

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M648617

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is 2 ⁶⁴⁸⁶¹⁷ - 1

has 195254 decimal digits

takes 0.010 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	6EF19222792DC6__	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	2⁶⁷	45.8112	70.1493%	1000000	30000000	0.0568	5.5093%	45.8680	71.7938%	1.6446%
PrimeNet	2⁴⁰	0.0000	50.0000%	6000	240000	0.0004	20.9486%	0.0004	60.4743%	10.4743%
GPU72	2⁴⁴	0.0000	54.5455%	11000	400000	0.0007	15.9544%	0.0007	61.7974%	7.2520%
Difference	+23	+45.8112	+15.6038%	+989000	+29600000	+0.0561	-10.4451%	+45.8673	+9.9964%	+9.9964%

Known prime factors (1 factor, 67.8 bits, 0.01045284% 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
648617	256745982405115174799	21	67.799	197918018187247 8400211 × 23561077	2008-01-24	8400211	23561077	47.078	0.2033	0.3767

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.191%
2002-01-22T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.412%
2002-03-10T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.001	-	-	0.748%
2002-05-05T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.222%
2002-07-06T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.005	-	-	1.841%
2002-10-07T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.600%
2003-06-01T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.487%
2016-03-17T18:50:15	alpertron	Manual testing	1000000	30000000	12	-		-	-	0.057	-	-	5.509%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-01-19T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07T09:02:12	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.015	-	-
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.030	-	-
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.059	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.524 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	8.524 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.769	0.000%
25	50000	1.616	19.866%
30	250000	0.131	87.697%
35	1000000	0.009	99.130%

ECM Summary

B1	B2	factor	curves	GHz-days
		256745982405115174799	1	0.00000e+0
50000	5000000		280	4.773
250000	25000000		44	3.750

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-25T22:56:00	Chad Davis	Bayes	50000	5000000						1	0.017
2007-11-07T15:26:00	James Heinrich	WHS	50000	5000000						1	0.017
2008-01-24T07:14:00	James Heinrich	Q6600			256745982405115174799	67.799		1		1	-
2014-09-19T17:12:00	Richard B. Woods	Puttputt	50000	5000000						7	0.119
2015-10-02T10:45:12	TJAOI	Manual testing	50000	5000000						90	1.534
2016-04-15T10:25:30	TJAOI	Manual testing	50000	5000000						90	1.534
2017-03-03T18:13:12	TJAOI	Manual testing	50000	5000000						91	1.551
2019-05-17T12:21:35	TJAOI	Manual testing	250000	25000000						44	3.750

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-09-14T00:00:00	ANONYMOUS	v4_computers	6EF19222792DC6__	0.010

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T13:51:19

Oliver Kruse

GTX-3

256745982405115174799

C05D752933811C__

2017-09-28T09:44:37

Oliver Kruse

Manual testing

256745982405115174799

C05D752933811C__

2017-11-08T23:06:23

kkmrkkblmbrbk

c4.large

256745982405115174799

C05D752933811C__

2020-04-19T21:02:56

Oliver Kruse

AddPrpType5

256745982405115174799

C6362237A9DDA7__

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 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T09:02:12+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