M371999 Mersenne number exponent details

Residue

Status

L-L

BC7B05E0DD141D__

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	79.8763	71.6418%	65536	6553600	0.0059	2.3804%	79.8822	72.3168%	0.6750%
PrimeNet	2⁴⁰	0.0000	52.5000%	3600	110000	0.0001	16.7460%	0.0001	60.4544%	7.9544%
GPU72	2⁴⁴	0.0000	56.8182%	6500	190000	0.0002	12.5056%	0.0002	62.2183%	5.4001%
Difference	+23	+79.8763	+14.8236%	+59036	+6363600	+0.0057	-10.1251%	+79.8820	+10.0985%	+10.0985%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

79.8763

71.6418%

65536

6553600

0.0059

2.3804%

79.8822

72.3168%

0.6750%

PrimeNet

2⁴⁰

0.0000

52.5000%

3600

110000

0.0001

16.7460%

0.0001

60.4544%

7.9544%

GPU72

2⁴⁴

0.0000

56.8182%

6500

190000

0.0002

12.5056%

0.0002

62.2183%

5.4001%

Difference

+23

+79.8763

+14.8236%

+59036

+6363600

+0.0057

-10.1251%

+79.8820

+10.0985%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
371999	783777067236792103	18	59.443	1053466631949 3 × 31 × 11327598193	2007-08-29	31	11327598193	0.3114	8.6754	16.203

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

371999

783777067236792103

59.443

1053466631949
3 × 31 × 11327598193

2007-08-29

11327598193

0.3114

8.6754

16.203

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2002-06-15T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.003	-	-	1.668%
2002-08-24T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.006	-	-	2.380%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2002-06-15T00:00:00

ANONYMOUS

v4_computers

32768

3276800

0.003

-

-

1.668%

2002-08-24T00:00:00

ANONYMOUS

v4_computers

65536

6553600

0.006

-

-

2.380%

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	-	-
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.006	-	-
2022-03-07T06:37:15	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.006	-	-
2001-03-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.026	-	-
2002-02-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.052	-	-
2004-01-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.103	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.506 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	425 / 100	4.250	1.396%
25	50000	425 / 280	1.518	21.859%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	10.506 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		783777067236792103	1	0.00000e+0
50000	5000000		281	2.949
250000	25000000		144	7.556

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-13T10:58:00	Team_Bundu	bundu1	50000	5000000						1	0.010
2007-08-29T05:38:00	Team_Bundu	bundu1			783777067236792103	59.443		1		1	-
2013-12-07T04:46:00	Richard B. Woods	Puttputt	50000	5000000						3	0.031
2013-12-08T01:39:00	Richard B. Woods	Puttputt	50000	5000000						3	0.031
2013-12-08T23:37:00	Richard B. Woods	Puttputt	50000	5000000						3	0.031
2014-10-17T12:39:00	TJAOI	Manual testing	50000	5000000						40	0.420
2015-02-27T10:16:00	TJAOI	Manual testing	50000	5000000						50	0.525
2016-01-04T14:30:41	TJAOI	Manual testing	50000	5000000						90	0.945
2016-11-11T16:51:01	TJAOI	Manual testing	50000	5000000						91	0.955
2018-04-13T12:44:49	TJAOI	Manual testing	250000	25000000						44	2.309
2020-07-27T10:56:30	TJAOI	Manual testing	250000	25000000						100	5.248

date	userid	compid	res64	spent (GHz-days)
2002-01-02T00:00:00	ANONYMOUS	v4_computers	BC7B05E0DD141D__	0.004

date

userid

compid

res64

spent (GHz-days)

2002-01-02T00:00:00

ANONYMOUS

v4_computers

BC7B05E0DD141D__

0.004

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-23T04:24:00

Oliver Kruse

Ollaptop

783777067236792103

3E2FD9E44B8A06__

2017-11-02T10:38:45

kkmrkkblmbrbk

c4.xlarge

783777067236792103

3E2FD9E44B8A06__

2020-04-18T15:21:12

Oliver Kruse

AddPrpType5

783777067236792103

9F414E17E70878__

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 = 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

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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