M432137 Mersenne number exponent details

Residue

Status

L-L

993766D4C63173__

double-checked

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	68.7604	71.6418%	3000000	100000000	0.1415	7.1713%	68.9019	73.6754%	2.0337%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	140000	0.0002	18.0748%	0.0002	61.0855%	8.5855%
GPU72	2⁴⁴	0.0000	56.8182%	8000	240000	0.0004	13.5803%	0.0004	62.6824%	5.8642%
Difference	+23	+68.7604	+14.8236%	+2992000	+99760000	+0.1411	-6.4090%	+68.9015	+10.9931%	+10.9931%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

68.7604

71.6418%

3000000

100000000

0.1415

7.1713%

68.9019

73.6754%

2.0337%

PrimeNet

2⁴⁰

0.0000

52.5000%

4500

140000

0.0002

18.0748%

0.0002

61.0855%

8.5855%

GPU72

2⁴⁴

0.0000

56.8182%

8000

240000

0.0004

13.5803%

0.0004

62.6824%

5.8642%

Difference

+23

+68.7604

+14.8236%

+2992000

+99760000

+0.1411

-6.4090%

+68.9015

+10.9931%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
432137	106082979603806718817	21	66.524	122742301172784 2⁴ × 3 × 2557131274433	2008-01-12	16	2557131274433	49.626	2,379.3	4,443.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

432137

106082979603806718817

66.524

122742301172784
2⁴ × 3 × 2557131274433

2008-01-12

2557131274433

49.626

2,379.3

4,443.8

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	-	-	1.713%
2002-08-31T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.007	-	-	2.438%
2016-03-17T18:48:01	alpertron	Manual testing	3000000	100000000	12	-		-	-	0.141	-	-	7.171%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-03-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.022	-	-
2002-02-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.044	-	-
2004-01-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.089	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.838 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:	12.838 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
		106082979603806718817	1	0.00000e+0
50000	5000000		279	3.585
250000	25000000		144	9.252

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-15T10:47:00	Team_Bundu	bundu1	50000	5000000						1	0.013
2007-09-03T18:59:00	Chad Davis	Bayes	50000	5000000						1	0.013
2007-10-25T09:07:00	ANONYMOUS	minister	50000	5000000						1	0.013
2008-01-12T14:48:00	Team_Bundu	bundu1			106082979603806718817	66.524		1		1	-
2013-12-13T22:02:00	Richard B. Woods	Puttputt	50000	5000000						9	0.116
2014-12-19T13:19:00	TJAOI	Manual testing	50000	5000000						36	0.463
2015-04-03T14:24:00	TJAOI	Manual testing	50000	5000000						50	0.643
2016-01-04T14:28:17	TJAOI	Manual testing	50000	5000000						90	1.157
2016-06-03T16:11:50	TJAOI	Manual testing	50000	5000000						91	1.169
2018-04-06T10:49:55	TJAOI	Manual testing	250000	25000000						44	2.827
2022-08-02T10:10:04	TJAOI	Manual testing	250000	25000000						100	6.425

date	userid	compid	res64	spent (GHz-days)
2002-02-24T00:00:00	ANONYMOUS	v4_computers	993766D4C63173__	0.005

date

userid

compid

res64

spent (GHz-days)

2002-02-24T00:00:00

ANONYMOUS

v4_computers

993766D4C63173__

0.005

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-23T23:06:52

Oliver Kruse

Doppelherz

106082979603806718817

4F123014E72D62__

2017-09-24T17:47:24

Oliver Kruse

Manual testing

106082979603806718817

4F123014E72D62__

2017-11-09T08:22:12

kkmrkkblmbrbk

c4.large

106082979603806718817

4F123014E72D62__

2020-04-18T18:19:00

Oliver Kruse

AddPrpType5

106082979603806718817

B3DB70FA5151CB__

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

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

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10⁰

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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