M1967429 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	15.1029	68.6567%	500000	1964033610	10.2468	10.0569%	25.3497	71.8089%	3.1522%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0014	2.4710%	0.0210	64.6878%	0.8947%
GPU72	2⁶²	0.3123	66.1290%	8000	100000	0.0012	1.1956%	0.3135	66.5340%	0.4049%
Difference	+5	+14.7907	+2.5277%	+492000	+1963933610	+10.2455	+8.8614%	+25.0362	+5.2749%	+5.2749%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.1029

68.6567%

500000

1964033610

10.2468

10.0569%

25.3497

71.8089%

3.1522%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0014

2.4710%

0.0210

64.6878%

0.8947%

GPU72

2⁶²

0.3123

66.1290%

8000

100000

0.0012

1.1956%

0.3135

66.5340%

0.4049%

Difference

+14.7907

+2.5277%

+492000

+1963933610

+10.2455

+8.8614%

+25.0362

+5.2749%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1967429	3435111359711	13	41.643	872995 5 × 174599	-	5	174599	2.918e-7	0.0009	0.0017
1967429	5012341940981762556671	22	72.086	1273830451056115 5 × 6719 × 37917263017	2021-08-14	6719	37917263017	959.10	196.95	367.85

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1967429

3435111359711

41.643

872995
5 × 174599

174599

2.918e-7

0.0009

0.0017

1967429

5012341940981762556671

72.086

1273830451056115
5 × 6719 × 37917263017

2021-08-14

6719

37917263017

959.10

196.95

367.85

exponent	prime factors	composite factor	digits	bits*
1967429	3435111359711 5012341940981762556671	17217952740222335290299466503682081	35	113.729

exponent

prime factors

composite factor

digits

bits*

1967429

3435111359711
5012341940981762556671

17217952740222335290299466503682081

113.729

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-12T03:19:59	Lisander Viaene	Desktop	500000	1964033610		-	skipped known factor: 3435111359711	-	-	10.25	-	-	10.057%

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.304 GHz-days
Estimated T-Level:	2.500

Digits	B1	Curves	Complete	FacMiss
20	11000	50 / 100	0.500	60.501%
25	50000	50 / 280	0.179	83.620%

New Calculation Method

Total ECM effort:	4.304 GHz-days
Estimated T-Level:	2.500

Digits	B1	Complete	FacMiss
20	11000	1.628	19.623%
25	50000	0.148	86.285%
30	250000	0.009	99.095%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	1.097
50000	5000000	5012341940981762556671	30	2.532
50000	6750000		7	0.674

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-21T12:37:10	alpertron	laptop2	50000	5000000						3	0.253
2019-03-22T10:43:16	MarkS	laptop64	50000	5000000						3	0.253
2021-01-21T06:25:27	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.591
2021-04-28T04:29:43	nordi	sweet16	50000	6750000						7	0.674
2021-08-14T23:14:04	MarkS	desktop-i7	50000	5000000	5012341940981762556671	72.086	30	2	2837083634998534	30	2.532

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T09:45:56

Oliver Kruse

GTX-2

3435111359711

5C6A6485CD5DA0__

2017-11-12T05:25:36

kkmrkkblmbrbk

old

3435111359711

5C6A6485CD5DA0__

2021-08-15T04:53:23

SRJ2877

LTOS

3435111359711

5012341940981762556671

42534055D39CAE47

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 = 1964033610 (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