M1965781 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	15.1156	68.6567%	-	-	-	-	15.1156	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0012	2.4706%	0.0207	64.6876%	0.8945%
GPU72	2⁶²	0.3125	66.1290%	8000	100000	0.0010	1.1953%	0.3136	66.5339%	0.4049%
Difference	+5	+14.8031	+2.5277%	-8000	-100000	-0.0010	-1.1953%	+14.8020	+2.1228%	+2.1228%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.1156

68.6567%

15.1156

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0012

2.4706%

0.0207

64.6876%

0.8945%

GPU72

2⁶²

0.3125

66.1290%

8000

100000

0.0010

1.1953%

0.3136

66.5339%

0.4049%

Difference

+14.8031

+2.5277%

-8000

-100000

-0.0010

-1.1953%

+14.8020

+2.1228%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1965781	969365926721	12	39.818	246560 2⁵ × 5 × 23 × 67	-	32	67	5.097e-8	2.667e-6	5.123e-6
1965781	1800709540749411961567	22	70.609	458013771816243 3 × 967 × 157881341543	2021-09-30	967	157881341543	219.58	676.64	1,263.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1965781

969365926721

39.818

246560
2⁵ × 5 × 23 × 67

5.097e-8

2.667e-6

5.123e-6

1965781

1800709540749411961567

70.609

458013771816243
3 × 967 × 157881341543

2021-09-30

967

157881341543

219.58

676.64

1,263.8

exponent	prime factors	composite factor	digits	bits*
1965781	969365926721 1800709540749411961567	1745546472723900038960197390331807	34	110.427

exponent

prime factors

composite factor

digits

bits*

1965781

969365926721
1800709540749411961567

1745546472723900038960197390331807

110.427

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.068 GHz-days
Estimated T-Level:	2.100

Digits	B1	Curves	Complete	FacMiss
20	11000	42 / 100	0.420	65.566%
25	50000	42 / 280	0.150	86.048%

New Calculation Method

Total ECM effort:	3.068 GHz-days
Estimated T-Level:	2.100

Digits	B1	Complete	FacMiss
20	11000	1.395	24.793%
25	50000	0.126	88.167%
30	250000	0.008	99.226%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		25	1.741
50000	5000000	1800709540749411961567	3	0.209
50000	6750000		7	0.556
50000	6900000		7	0.562

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-07-13T15:12:00	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-23T01:38:29	ATH	ec2-ECMCF	50000	5000000						3	0.209
2021-01-06T22:42:39	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.488
2021-04-02T18:30:57	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.488
2021-07-16T23:34:01	Daniil Tsarkov	9900KF	50000	5000000						7	0.488
2021-09-30T01:17:35	MarkS	laptop64	50000	5000000	1800709540749411961567	70.609	3	2	2814880159147500	3	0.209
2021-11-10T03:41:47	Dylan Delgado	colab	50000	6750000						7	0.556
2022-04-11T10:06:37	MarkS	desktop-i7	50000	6900000						7	0.562

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T09:21:24

Oliver Kruse

GTX-0

969365926721

437008369D90B1__

2017-11-11T22:31:44

ATH

ec2-1xf

969365926721

437008369D90B1__

2021-10-01T11:13:07

JackBlock

Win10

969365926721

1800709540749411961567

40E27AA7F5F5EB57

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

10⁰

10¹

10²

10³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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