M717581 Mersenne number exponent details

≡

M717581

<<<

>>>

is 2 ⁷¹⁷⁵⁸¹ - 1

has 216014 decimal digits

takes 0.014 GHz-days to do one PRP test

Last-known PrimeNet details:
0 L-L tests remaining

	Residue	Status
L-L	F46F56904012D9__	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	41.4085	70.1493%	500000	15000000	0.0374	4.5231%	41.4458	74.6723%	24.6723%
PrimeNet	2⁴⁰	0.0000	50.0000%	6500	260000	0.0006	21.5316%	0.0006	71.5316%	21.5316%
GPU72	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5468%	0.0010	71.0923%	16.5468%
Difference	+23	+41.4084	+15.6038%	+488000	+14550000	+0.0363	-12.0237%	+41.4448	+3.5801%	+3.5801%

Known prime factors (1 factor, 68.4 bits, 0.00953737% known):

Remaining cofactor is not a probable-prime

								GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
717581	399936211771065892513	21	68.438	278669733292176 2⁴ × 3 × 107 × 59239 × 915919	59239	915919	2003-06-17	101.02	0.0031	0.0035

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	-	-	0.197%
2002-01-28T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.423%
2002-03-16T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.765%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.246%
2002-07-14T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.874%
2002-11-09T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.641%
2016-03-17T18:50:43	alpertron	Manual testing	500000	15000000	12	-		-	-	0.037	-	-	4.523%
2021-03-16T10:40:11	manrus	Manual testing	59239	915919	6		399936211771065892513	21	68.438	0.003	0.029	0.006	1.639%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-06-17T00:00:00	ANONYMOUS	v4_computers	?	?	399936211771065892513	68.438	21	17.96	0.030	37.52
2003-08-25T00:00:00	ANONYMOUS	v4_computers	?	?	399936211771065892513	68.438	21	17.96	0.030	37.52
1999-12-15T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2000-05-24T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁵		-	-	0.007	-	-
2000-05-31T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁵		-	-	0.007	-	-
2001-04-01T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁶		-	-	0.013	-	-
2001-10-20T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁷		-	-	0.027	-	-

ECM factoring results:

Total ECM effort:	11.630 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	337 / 100	3.370	3.381%
25	50000	337 / 280	1.204	29.947%
30	250000	44 / 640	0.069	93.351%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	6.352
50000	6750000	12	0.305
250000	25000000	44	4.973

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-23T13:48:14	TJAOI	Manual testing	50000	5000000						100	2.261
2016-07-01T10:29:50	TJAOI	Manual testing	50000	5000000						90	2.034
2017-04-28T21:36:01	TJAOI	Manual testing	50000	5000000						91	2.057
2018-11-23T13:32:55	TJAOI	Manual testing	250000	25000000						44	4.973
2020-12-22T23:16:11	masser	Manual testing	50000	6750000						6	0.152
2020-12-22T23:23:11	masser	Manual testing	50000	6750000						6	0.152

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-10-07T00:00:00	ANONYMOUS	v4_computers	F46F56904012D9__	0.014

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T16:37:57

Oliver Kruse

GTX-0

399936211771065892513

EC0E9AFE382394__

2017-10-13T15:47:50

Oliver Kruse

Threadripper

EC0E9AFE382394__

2017-12-16T09:25:22

ATH

ec2-1xf

399936211771065892513

EC0E9AFE382394__

2020-04-20T17:52:19

Oliver Kruse

AddPrpType5

399936211771065892513

8DB2117645025E__

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 = 500000, B2 = 15000000 (stage 2)

B1 = 500000 (stage 1)

B1 = 65537, B2 = 6553700 (stage 2)

B1 = 32768, B2 = 3276800 (stage 2)

B1 = 59239, B2 = 915919 (stage 2)

B1 = 16384, B2 = 1638400 (stage 2)

B1 = 65537 (stage 1)

B1 = 59239 (stage 1)

B1 = 8192, B2 = 819200 (stage 2)

B1 = 32768 (stage 1)

B1 = 4096, B2 = 409600 (stage 2)

B1 = 16384 (stage 1)

B1 = 2000, B2 = 200000 (stage 2)

B1 = 8192 (stage 1)

B1 = 4096 (stage 1)

B1 = 2000 (stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-03-16T10:40:11+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	<	123M	PrimeNet wavefront