M509867 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	58.2778	71.6418%	1500000	50000000	0.0876	6.1123%	58.3654	73.3751%	1.7333%
PrimeNet	2⁴⁰	0.0000	52.5000%	5000	170000	0.0003	19.1446%	0.0003	61.5937%	9.0937%
GPU72	2⁴⁴	0.0000	56.8182%	9000	300000	0.0005	14.5552%	0.0005	63.1034%	6.2852%
Difference	+23	+58.2778	+14.8236%	+1491000	+49700000	+0.0871	-8.4429%	+58.3648	+10.2717%	+10.2717%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
509867	58486074638415289653119	23	75.631	57354245948860477 17 × 3373779173462381	2009-09-20	17	3373779173462381	27,017	3,886,875	7,259,600

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.764%
2002-08-31T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.503%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.370%
2016-03-16T12:41:38	alpertron	Manual testing	1500000	50000000	12	-		-	-	0.088	-	-	6.112%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-08T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07T07:50:56	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.005	-	-
2001-04-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.019	-	-
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.038	-	-
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.075	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.056 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	423 / 100	4.230	1.425%
25	50000	423 / 280	1.511	22.016%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	16.056 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.822	0.000%
25	50000	3.021	4.875%
30	250000	0.287	75.083%
35	1000000	0.022	97.834%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		58486074638415289653119	1	0.00000e+0
50000	5000000		279	4.484
250000	25000000		144	11.57

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-18T02:52:00	Chad Davis	Bayes	50000	5000000						1	0.016
2007-09-14T11:36:00	Chad Davis	Bayes	50000	5000000						1	0.016
2008-01-03T22:51:00	Steve Scott		50000	5000000						1	0.016
2008-01-04T02:08:00	Steve Scott	Abit	50000	5000000						1	0.016
2008-01-04T02:31:00	Steve Scott		50000	5000000						1	0.016
2008-05-03T16:46:00	Sturle Sunde	v17	50000	5000000						3	0.048
2008-10-01T19:22:00	Sturle Sunde	v1	50000	5000000						3	0.048
2008-12-02T01:36:00	Sturle Sunde	v21	50000	5000000						3	0.048
2009-02-07T06:45:00	Sturle Sunde	v23	50000	5000000						3	0.048
2009-03-18T18:10:00	James Heinrich	WHS	50000	5000000						3	0.048
2009-05-20T15:15:00	JPH	diablo	50000	5000000						3	0.048
2009-07-03T20:47:00	JPH	diablo	50000	5000000						3	0.048
2009-07-12T06:07:00	Architects Cubed	m1_45	50000	5000000						3	0.048
2009-08-17T00:32:00	JimBa	NASsrvr	50000	5000000						3	0.048
2009-09-20T01:04:00	JimBa	ISAserv			58486074638415289653119	75.631		1		1	-
2015-06-12T09:29:00	TJAOI	Manual testing	50000	5000000						66	1.061
2016-03-04T13:13:35	TJAOI	Manual testing	50000	5000000						90	1.447
2016-12-23T15:34:55	TJAOI	Manual testing	50000	5000000						91	1.463
2018-11-02T13:30:54	TJAOI	Manual testing	250000	25000000						44	3.536
2021-01-22T13:10:19	TJAOI	Manual testing	250000	25000000						100	8.036

date	userid	compid	res64	spent (GHz-days)
2002-04-28T00:00:00	ANONYMOUS	v4_computers	372409D0A5D81004	0.007

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T09:34:42

Oliver Kruse

GTX-2

58486074638415289653119

7259129704DA85__

2017-09-28T09:42:23

Oliver Kruse

Manual testing

58486074638415289653119

7259129704DA85__

2017-11-07T06:15:55

kkmrkkblmbrbk

c4.xlarge

58486074638415289653119

7259129704DA85__

2020-04-19T00:47:19

Oliver Kruse

AddPrpType5

58486074638415289653119

E9116D3C46C1E5__

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 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (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 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

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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