M1915007 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	15.5163	68.6567%	500000	15000000	0.1015	5.0964%	15.6178	70.2541%	1.5974%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0913%	0.0114	64.2968%	1.1389%
GPU72	2⁶¹	0.1604	65.5738%	10000	170000	0.0015	1.7606%	0.1619	66.1799%	0.6061%
Difference	+6	+15.3559	+3.0829%	+490000	+14830000	+0.1000	+3.3357%	+15.4559	+4.0742%	+4.0742%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.5163

68.6567%

500000

15000000

0.1015

5.0964%

15.6178

70.2541%

1.5974%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0913%

0.0114

64.2968%

1.1389%

GPU72

2⁶¹

0.1604

65.5738%

10000

170000

0.0015

1.7606%

0.1619

66.1799%

0.6061%

Difference

+15.3559

+3.0829%

+490000

+14830000

+0.1000

+3.3357%

+15.4559

+4.0742%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1915007	84697183499118103	17	56.233	22114066293 3² × 11 × 17 × 373 × 35227	-	373	35227	0.0072	0.0002	0.0003
1915007	27768509757071341992863	23	74.556	7250237141971633 1087 × 6669951372559	2021-10-26	1087	6669951372559	2,314.8	28,586	53,390

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1915007

84697183499118103

56.233

22114066293
3² × 11 × 17 × 373 × 35227

373

35227

0.0072

0.0002

0.0003

1915007

27768509757071341992863

74.556

7250237141971633
1087 × 6669951372559

2021-10-26

1087

6669951372559

2,314.8

28,586

53,390

exponent	prime factors	composite factor	digits	bits*
1915007	84697183499118103 27768509757071341992863	2351914566391722909911541256071020098889	40	130.789

exponent

prime factors

composite factor

digits

bits*

1915007

84697183499118103
27768509757071341992863

2351914566391722909911541256071020098889

130.789

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:42:25	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 84697183499118103	-	-	0.101	-	-	5.096%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:42:25

alpertron

Manual testing

500000

15000000

skipped known factor: 84697183499118103

0.101

-

-

5.096%

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.584 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	21.584 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.084	0.011%
25	50000	0.806	44.654%
30	250000	0.050	95.125%
35	1000000	0.002	99.770%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	1.875
50000	5000000	27768509757071341992863	1	0.069
50000	5799953		14	1.034
50000	8000000		216	18.61

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T19:28:01	alpertron	laptop2	50000	5000000						3	0.208
2019-01-31T02:54:47	tottenhoff	2011pc	50000	5000000						3	0.208
2020-10-28T11:47:45	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2021-01-19T18:24:21	seatsea	dt	50000	5799953						7	0.517
2021-04-19T19:37:39	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-07-14T09:01:41	seatsea	Manual testing	50000	5799953						7	0.517
2021-10-26T02:24:43	MarkS	laptop64	50000	5000000	27768509757071341992863	74.556	1	2	7613184926042272	1	0.069
2021-11-07T19:11:48	MarkS	desktop-i7	50000	5000000						7	0.486
2022-01-06T11:59:22	TJAOI	Manual testing	50000	8000000						216	18.61

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:14:46

alpertron

Manual testing

84697183499118103

64CF26B15995E1__

2017-10-20T04:22:48

Oliver Kruse

Threadripper

84697183499118103

64CF26B15995E1__

2021-10-26T06:36:17

MarkS

desktop-i7

84697183499118103

27768509757071341992863

4C5A18D9EEAB6DFE

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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