M474899 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	62.5689	71.6418%	10000000	250000000	0.3941	9.0548%	62.9630	74.2096%	2.5678%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	160000	0.0002	18.6576%	0.0002	61.3623%	8.8623%
GPU72	2⁴⁴	0.0000	56.8182%	8000	260000	0.0004	13.9327%	0.0004	62.8346%	6.0164%
Difference	+23	+62.5689	+14.8236%	+9992000	+249740000	+0.3937	-4.8779%	+62.9626	+11.3750%	+11.3750%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
474899	19693408906132706191	20	64.094	20734312881405 3 × 5 × 4909 × 281582303	2009-08-30	4909	281582303	8.4912	0.2621	0.4893

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.005	-	-	2.478%
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.742%
2002-09-14T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.007	-	-	2.475%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.014	-	-	3.336%
2009-08-07T16:08:00	James Hintz	home2	10000000	250000000		-		-	-	0.394	-	-	9.055%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.005	-	-
2022-03-07T07:41:22	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.005	-	-
2001-03-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.020	-	-
2002-01-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.040	-	-
2003-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.081	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.909 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:	12.909 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
		19693408906132706191	1	0.00000e+0
50000	5000000		279	3.605
250000	25000000		144	9.304

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-17T03:00:00	ANONYMOUS	Bayes	50000	5000000						1	0.013
2007-09-08T22:49:00	Chad Davis	Bayes	50000	5000000						1	0.013
2007-12-19T02:12:00	Steve Scott	Abit	50000	5000000						1	0.013
2007-12-19T03:30:00	Steve Scott	Abit	50000	5000000						1	0.013
2007-12-19T03:58:00	Steve Scott	Abit	50000	5000000						1	0.013
2008-02-29T05:51:00	David Campeau		50000	5000000						3	0.039
2008-09-18T22:43:00	Sturle Sunde	v21	50000	5000000						3	0.039
2008-11-18T11:50:00	Sturle Sunde	v17	50000	5000000						3	0.039
2009-01-13T21:55:00	Sturle Sunde	v22	50000	5000000						3	0.039
2009-03-02T19:16:00	Dalos Lee	dalosdesk	50000	5000000						3	0.039
2009-04-07T16:40:00	James Hintz	04_060209	50000	5000000						3	0.039
2009-06-13T20:42:00	JPH	diablo	50000	5000000						3	0.039
2009-07-08T12:55:00	Architects Cubed	m1_42	50000	5000000						3	0.039
2009-07-25T20:47:00	JimBa	NASsrvr	50000	5000000						3	0.039
2009-08-30T05:41:00	JimBa	CIT3srvr			19693408906132706191	64.094		1		1	-
2015-05-08T10:38:00	TJAOI	Manual testing	50000	5000000						66	0.853
2016-02-26T13:30:07	TJAOI	Manual testing	50000	5000000						90	1.163
2016-09-09T13:47:48	TJAOI	Manual testing	50000	5000000						91	1.176
2018-06-15T13:09:26	TJAOI	Manual testing	250000	25000000						44	2.843
2020-11-27T10:30:42	TJAOI	Manual testing	250000	25000000						100	6.461

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-26T05:35:37

Oliver Kruse

Doppelherz

19693408906132706191

167AA19ACBC963__

2017-09-27T07:35:30

Oliver Kruse

Manual testing

19693408906132706191

167AA19ACBC963__

2017-11-09T06:39:56

kkmrkkblmbrbk

c4.large

19693408906132706191

167AA19ACBC963__

2020-04-18T10:36:56

Oliver Kruse

AddPrpType5

19693408906132706191

8880314A5F9C72__

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 = 10000000, B2 = 250000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

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

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

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

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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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