M467431 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	63.5686	71.6418%	3000000	100000000	0.1415	7.2288%	63.7101	73.6917%	2.0500%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	150000	0.0002	18.4413%	0.0002	61.2596%	8.7596%
GPU72	2⁴⁴	0.0000	56.8182%	8000	260000	0.0004	13.9047%	0.0004	62.8225%	6.0043%
Difference	+23	+63.5686	+14.8236%	+2992000	+99740000	+0.1411	-6.6759%	+63.7097	+10.8693%	+10.8693%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
467431	213072165532045555775329513	27	87.461	227918308297957940076 2² × 3 × 31 × 7297 × 83963769282839	2009-10-24	7297	83963769282839	79,767,687	78,124	145,913

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.173%
2002-01-02T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.002	-	-	1.492%
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.737%
2002-09-14T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.007	-	-	2.469%
2009-08-27T03:58:00	Carsten Kossendey	leela	467431	467431		-		-	-	0.008	-	-	1.573%
unknown			3000000	100000000		-		-	-	0.141	-	-	7.229%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.005	-	-
2022-03-07T07:41:13	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.005	-	-
2001-03-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.021	-	-
2002-02-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.041	-	-
2004-01-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.082	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.884 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	422 / 100	4.220	1.439%
25	50000	422 / 280	1.507	22.095%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	12.884 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.783	0.000%
25	50000	3.017	4.892%
30	250000	0.286	75.100%
35	1000000	0.022	97.835%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		213072165532045555775329513	1	0.00000e+0
50000	5000000		278	3.589
250000	25000000		144	9.295

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-16T22:13:00	ANONYMOUS	Bayes	50000	5000000						1	0.013
2007-09-07T21:11:00	Team_Bundu	bundu1	50000	5000000						1	0.013
2007-12-06T12:29:00	Sturle Sunde	minister	50000	5000000						1	0.013
2007-12-06T19:29:00	Sturle Sunde	minister	50000	5000000						1	0.013
2007-12-06T19:34:00	James Heinrich	WHS	50000	5000000						1	0.013
2008-02-18T22:24:00	Chad Davis	Bayes	50000	5000000						3	0.039
2008-09-17T02:50:00	Sturle Sunde	v21	50000	5000000						3	0.039
2008-11-13T20:41:00	Jayson King	atlas	50000	5000000						3	0.039
2009-01-09T03:11:00	Sturle Sunde	v23	50000	5000000						3	0.039
2009-02-25T23:18:00	Sturle Sunde	v23	50000	5000000						3	0.039
2009-03-31T15:50:00	Ryan Schulz	T7400	50000	5000000						3	0.039
2009-06-05T21:53:00	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.039
2009-07-07T19:59:00	Architects Cubed	m1_75	50000	5000000						3	0.039
2009-07-12T01:14:00	Architects Cubed	m1_02	50000	5000000						3	0.039
2009-08-16T19:13:00	JimBa	NASsrvr	50000	5000000						3	0.039
2009-09-18T01:54:00	JimBa	ISAserv	50000	5000000						3	0.039
2009-10-08T17:21:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.039
2009-10-24T20:23:00	JimBa	ISAserv			213072165532045555775329513	87.461		1		1	-
2015-05-08T10:37:00	TJAOI	Manual testing	50000	5000000						56	0.723
2016-02-12T13:32:06	TJAOI	Manual testing	50000	5000000						90	1.162
2016-06-17T16:31:40	TJAOI	Manual testing	50000	5000000						91	1.175
2018-05-04T12:07:00	TJAOI	Manual testing	250000	25000000						44	2.840
2020-10-09T08:30:27	TJAOI	Manual testing	250000	25000000						100	6.455

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-25T19:15:31

Oliver Kruse

Doppelherz

213072165532045555775329513

EC5B1AA8A831C4__

2017-09-27T07:34:59

Oliver Kruse

Manual testing

213072165532045555775329513

EC5B1AA8A831C4__

2017-11-07T06:19:12

kkmrkkblmbrbk

c4.xlarge

213072165532045555775329513

EC5B1AA8A831C4__

2020-04-18T10:23:39

Oliver Kruse

AddPrpType5

213072165532045555775329513

5491F8983B008C__

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 467431 (P-1 stage 1)

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

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

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

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

B1 = 2000 (P-1 stage 1)

10²

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10¹⁰

10¹¹

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10¹³

10¹⁴

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