M1952689 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	15.2169	68.6567%	500000	15000000	0.1015	5.1083%	15.3184	70.2578%	1.6011%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4674%	0.0209	64.6865%	0.8934%
GPU72	2⁶²	0.3146	66.1290%	8000	90000	0.0010	1.1534%	0.3156	66.5197%	0.3907%
Difference	+5	+14.9023	+2.5277%	+492000	+14910000	+0.1005	+3.9549%	+15.0028	+3.7381%	+3.7381%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2169

68.6567%

500000

15000000

0.1015

5.1083%

15.3184

70.2578%

1.6011%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4674%

0.0209

64.6865%

0.8934%

GPU72

2⁶²

0.3146

66.1290%

8000

90000

0.0010

1.1534%

0.3156

66.5197%

0.3907%

Difference

+14.9023

+2.5277%

+492000

+14910000

+0.1005

+3.9549%

+15.0028

+3.7381%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1952689	874804673	9	29.704	224 2⁵ × 7	-	32	32	3.840e-11	2.517e-6	5.123e-6
1952689	2047297067928086582519	22	70.794	524225073201131 27691 × 18931243841	2020-11-24	27691	18931243841	124.25	81.137	151.54

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1952689

874804673

29.704

224
2⁵ × 7

3.840e-11

2.517e-6

5.123e-6

1952689

2047297067928086582519

70.794

524225073201131
27691 × 18931243841

2020-11-24

27691

18931243841

124.25

81.137

151.54

exponent	prime factors	composite factor	digits	bits*
1952689	874804673 2047297067928086582519	1790985042042688570336221311287	31	100.499

exponent

prime factors

composite factor

digits

bits*

1952689

874804673
2047297067928086582519

1790985042042688570336221311287

100.499

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:19:14	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 874804673	-	-	0.101	-	-	5.108%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:19:14

alpertron

Manual testing

500000

15000000

skipped known factor: 874804673

0.101

-

-

5.108%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.936 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	20.936 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	9.042	0.012%
25	50000	0.804	44.750%
30	250000	0.050	95.137%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	2.505
50000	5000000	2047297067928086582519	1	0.070
50000	6750000		7	0.556
50000	7500000		213	17.81

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-07-18T07:27:17	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-30T03:33:29	alan145	Bear1	50000	5000000						3	0.209
2020-11-24T09:25:01	MarkS	desktop-i7	50000	5000000	2047297067928086582519	70.794	1	2	4015978728564854	1	0.070
2020-12-03T16:49:46	Poao	servarica-CA	50000	5000000						7	0.487
2021-03-08T16:14:55	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.487
2021-07-13T12:34:27	happy5214	Focus	50000	6750000						7	0.556
2021-09-25T16:27:40	MarkS	desktop-i7	50000	5000000						11	0.765
2022-04-10T15:24:23	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-05-12T09:17:49	TJAOI	Manual testing	50000	7500000						213	17.81

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T06:03:56

Oliver Kruse

GTX-3

874804673

FD017CDA306BAA__

2017-11-11T14:16:06

kkmrkkblmbrbk

c4.xlarge

874804673

FD017CDA306BAA__

2020-11-24T15:26:45

mrh

874804673

2047297067928086582519

59CE69BA37F3D648

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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