M816587 Mersenne number exponent details

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M816587

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is 2 ⁸¹⁶⁵⁸⁷ - 1

has 245818 decimal digits

takes 0.016 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	36.3879	70.1493%	300000	10000000	0.0240	3.9589%	36.4119	71.3310%	1.1818%
PrimeNet	2⁴⁰	0.0000	50.0000%	7000	300000	0.0007	22.3608%	0.0007	61.1804%	11.1804%
GPU72	2⁴⁴	0.0000	54.5455%	14000	550000	0.0013	17.4916%	0.0013	62.4962%	7.9507%
Difference	+23	+36.3879	+15.6038%	+286000	+9450000	+0.0227	-13.5327%	+36.4107	+8.8348%	+8.8348%

Known prime factors (1 factor, 58.6 bits, 0.00717067% 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
816587	423387199468833049	18	58.555	259241942052 2² × 3² × 31 × 232295647	2007-09-03	31	232295647	0.0691	0.3665	0.6846

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	-	-	0.205%
2002-02-10T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.437%
2002-04-07T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.787%
2002-05-18T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.279%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.917%
2002-11-24T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.695%
2003-07-21T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.601%
2016-03-17T18:52:17	alpertron	Manual testing	300000	10000000	12	-		-	-	0.024	-	-	3.959%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2000-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.024	-	-
2003-08-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.047	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.468 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.468 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		423387199468833049	1	0.00000e+0
50000	5000000		281	6.432
250000	25000000		44	5.036

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-03T02:54:00	Team_Bundu	bundu1			423387199468833049	58.555		1		1	-
2015-11-26T17:20:07	Richard B. Woods	Puttputt	50000	5000000						1	0.023
2015-12-11T11:34:12	TJAOI	Manual testing	50000	5000000						100	2.289
2016-09-02T12:17:32	TJAOI	Manual testing	50000	5000000						89	2.037
2017-07-14T09:30:58	TJAOI	Manual testing	50000	5000000						91	2.083
2019-08-19T13:17:10	TJAOI	Manual testing	250000	25000000						44	5.036

Lucas-Lehmer results:
No L-L results for M816587

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T02:09:47

Oliver Kruse

GTX-2

423387199468833049

B897F39350E9E3__

2017-10-14T01:14:17

Oliver Kruse

GTX-1

B897F39350E9E3__

2017-12-17T14:58:30

ATH

ec2-1xf

423387199468833049

B897F39350E9E3__

2020-04-21T10:43:04

Oliver Kruse

AddPrpType5

423387199468833049

FB40A50C7EC82F__

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

B1 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

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

B1 = 131072 (P-1 stage 1)

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

B1 = 65537 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-21T10:43:04+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