M286397 Mersenne number exponent details

is 2 ²⁸⁶³⁹⁷ - 1

has 86215 decimal digits

takes 0.002 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	103.7508	71.6418%	262144	26214400	0.0166	4.0383%	103.7674	72.7870%	1.1452%
PrimeNet	2⁴⁰	0.0000	52.5000%	3000	80000	0.0001	15.0584%	0.0001	59.6528%	7.1528%
GPU72	2⁴⁴	0.0000	56.8182%	5000	130000	0.0001	10.8755%	0.0001	61.5144%	4.6963%
Difference	+23	+103.7508	+14.8236%	+257144	+26084400	+0.0165	-6.8372%	+103.7673	+11.2726%	+11.2726%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
286397	1711334904435820639	19	60.570	2987696980827 3² × 13 × 25535871631	2007-08-27	13	25535871631	0.6369	13.785	25.747

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-05-06T00:00:00	ANONYMOUS	v4_computers	100000	4000000		-		-	-	0.003	-	-	2.292%
2001-07-07T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.006	-	-	2.768%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.002	-	-	1.591%
2002-08-17T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.004	-	-	2.283%
2003-03-16T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.008	-	-	3.102%
2003-11-28T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.017	-	-	4.038%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	286397	286397		-		-	-	0.003	-	-	1.148%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-11-24T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-
2000-05-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.008	-	-
2022-03-07T06:11:41	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.008	-	-
2001-02-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.034	-	-
2002-03-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.067	-	-
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.134	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.324 GHz-days
Estimated T-Level:	28.172

Digits	B1	Curves	Complete	FacMiss
20	11000	687 / 100	6.870	0.100%
25	50000	687 / 280	2.454	8.561%
30	250000	406 / 640	0.634	53.000%

New Calculation Method

Total ECM effort:	18.324 GHz-days
Estimated T-Level:	28.172

Digits	B1	Complete	FacMiss
20	11000	49.971	0.000%
25	50000	7.039	0.088%
30	250000	0.733	48.066%
35	1000000	0.060	94.187%
40	3000000	0.004	99.601%

ECM Summary

B1	B2	factor	curves	GHz-days
		1711334904435820639	1	0.00000e+0
50000	5000000		281	2.056
250000	25000000		158	5.779
250000	35250000		7	0.291
250000	36535620		7	0.295
250000	36750000		234	9.90

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-11T00:01:00	George Woltman	D_P4Debug	50000	5000000						1	0.007
2007-08-27T13:04:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-08-27T20:28:00	Team_Bundu	bundu1			1711334904435820639	60.570		1		1	-
2014-09-05T15:14:00	TJAOI	Manual testing	50000	5000000						48	0.351
2015-01-09T16:39:00	TJAOI	Manual testing	50000	5000000						50	0.366
2015-10-30T13:18:17	TJAOI	Manual testing	50000	5000000						90	0.658
2016-03-24T20:21:11	TJAOI	Manual testing	50000	5000000						91	0.666
2019-01-04T14:23:58	TJAOI	Manual testing	250000	25000000						44	1.609
2020-04-29T12:26:56	Greg	azure2	250000	25000000						3	0.110
2020-05-03T19:57:12	Oliver Kruse	IOS-2	250000	25000000						3	0.110
2020-05-09T18:57:15	Greg Hogan	azure7	250000	25000000						3	0.110
2020-05-29T15:16:03	kracker	O0	250000	25000000						3	0.110
2020-06-15T21:24:08	nordi	sweet16	250000	25000000						3	0.110
2020-06-26T04:13:07	Chang Chia-Tche	exbpc13	250000	25000000						3	0.110
2020-07-05T20:37:25	-Anonymous-	aws-nano	250000	25000000						3	0.110
2020-07-20T12:24:55	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.110
2020-07-31T10:27:51	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.110
2020-09-09T06:23:56	Chang Chia-Tche	exbpc13	250000	25000000						7	0.256
2020-10-21T15:48:06	Chang Chia-Tche	exbpc13	250000	25000000						7	0.256
2020-11-05T09:46:39	nordi	sweet16	250000	25000000						7	0.256
2020-12-21T12:43:13	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.256
2021-01-01T10:28:18	TJAOI	Manual testing	250000	25000000						52	1.902
2021-12-04T03:38:34	Luminescence	W-2295	250000	36750000						7	0.296
2022-02-25T00:03:57	JackBlock	school10	250000	25000000						7	0.256
2022-04-17T12:56:19	Alex Kruppa	lily	250000	35250000						7	0.291
2022-05-30T06:25:26	debrouxl	z400	250000	36535620						7	0.295
2022-06-25T04:34:56	debrouxl	dl380g9-1	250000	36750000						7	0.296
2022-07-19T07:53:50	nordi	sweet16_ccx2	250000	36750000						220	9.310

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-03-03T00:00:00	ANONYMOUS	v4_computers	291ACDFF5C49CD__	0.002

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T12:26:45

Oliver Kruse

Ollaptop

1711334904435820639

F87A8B3B4B2F19__

2017-09-22T20:36:24

Oliver Kruse

Manual testing

1711334904435820639

F87A8B3B4B2F19__

2017-10-12T19:41:35

Oliver Kruse

GTX-2

F87A8B3B4B2F19__

2017-11-06T20:05:22

kkmrkkblmbrbk

c4.xlarge

1711334904435820639

F87A8B3B4B2F19__

2020-04-17T22:11:39

Oliver Kruse

AddPrpType5

1711334904435820639

1330740BA9F6D9__

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 = 262144, B2 = 26214400 (P-1 stage 2)

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

B1 = 100000, B2 = 10000000 (P-1 stage 2)

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

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 286397 (P-1 stage 1)

B1 = 262144 (P-1 stage 1)

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

B1 = 131072 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵³

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-07-19T07:53:50+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