M1966127 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	15.1129	68.6567%	500000	1964033610	10.2468	10.0563%	25.3597	71.8087%	3.1520%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0014	2.4707%	0.0210	64.6877%	0.8946%
GPU72	2⁶²	0.3125	66.1290%	8000	100000	0.0012	1.1954%	0.3137	66.5339%	0.4049%
Difference	+5	+14.8004	+2.5277%	+492000	+1963933610	+10.2455	+8.8609%	+25.0460	+5.2748%	+5.2748%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.1129

68.6567%

500000

1964033610

10.2468

10.0563%

25.3597

71.8087%

3.1520%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0014

2.4707%

0.0210

64.6877%

0.8946%

GPU72

2⁶²

0.3125

66.1290%

8000

100000

0.0012

1.1954%

0.3137

66.5339%

0.4049%

Difference

+14.8004

+2.5277%

+492000

+1963933610

+10.2455

+8.8609%

+25.0460

+5.2748%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1966127	519057529	9	28.951	132 2² × 3 × 11	-	4	11	1.871e-11	4.177e-7	7.761e-7
1966127	14549339801	11	33.760	3700 2² × 5² × 37	2008-07-15	25	37	1.048e-9	2.446e-6	4.851e-6
1966127	29977306474712467616407	23	74.666	7623441027642789 3² × 847049003071421	2021-01-21	9	847049003071421	3,390.2	4,399,784	8,217,572

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1966127

519057529

28.951

132
2² × 3 × 11

1.871e-11

4.177e-7

7.761e-7

1966127

14549339801

33.760

3700
2² × 5² × 37

2008-07-15

1.048e-9

2.446e-6

4.851e-6

1966127

29977306474712467616407

74.666

7623441027642789
3² × 847049003071421

2021-01-21

847049003071421

3,390.2

4,399,784

8,217,572

exponent	prime factors	composite factor	digits	bits*
1966127	519057529 14549339801	7551944365688411729	19	62.712
1966127	519057529 29977306474712467616407	15559946624839954426464737278303	32	103.618
1966127	14549339801 29977306474712467616407	436150018219309105122313965715007	33	108.427
1966127	519057529 14549339801 29977306474712467616407	226386950730219564191989529806222251637703	42	137.378

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-04-12T01:31:23	Lisander Viaene	Desktop	500000	1964033610		-	skipped known factor: 519057529 skipped known factor: 14549339801	-	-	10.25	-	-	10.056%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-04-12T01:31:23

Lisander Viaene

Desktop

500000

1964033610

skipped known factor: 519057529
skipped known factor: 14549339801

10.25

-

-

10.056%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:48:00	J Feitsma	Manual testing	?	?	14549339801	33.760	11	4.66124e-10	0.282	1.01760e-9

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:48:00

J Feitsma

Manual testing

14549339801

33.760

4.66124e-10

0.282

1.01760e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.144 GHz-days
Estimated T-Level:	24.714

Digits	B1	Curves	Complete	FacMiss
20	11000	264 / 100	2.640	7.042%
25	50000	264 / 280	0.943	38.886%

New Calculation Method

Total ECM effort:	26.144 GHz-days
Estimated T-Level:	24.714

Digits	B1	Complete	FacMiss
20	11000	10.891	0.002%
25	50000	1.029	35.734%
30	250000	0.066	93.649%
35	1000000	0.003	99.692%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.279
50000	5306465		7	0.605
50000	6750000		7	0.674
50000	6750000	29977306474712467616407	2	0.193
50000	7069850		7	0.689
50000	7500000		214	21.70

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-20T21:26:40	ATH	ec2-1xe	50000	5000000						3	0.253
2019-03-19T11:03:00	MarkS	laptop64	50000	5000000						3	0.253
2021-01-21T05:19:29	seatsea	dt	50000	6750000	29977306474712467616407	74.666	2	2	7934562962054108	2	0.193
2021-02-11T21:20:00	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.591
2021-05-27T22:55:51	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.591
2021-08-29T16:20:43	Dylan Delgado	colab	50000	6750000						7	0.674
2021-12-23T12:05:00	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.591
2022-05-14T00:20:20	debrouxl	o9020	50000	5306465						7	0.605
2022-07-06T11:17:55	debrouxl	o9020	50000	7069850						7	0.689
2022-08-02T10:12:46	TJAOI	Manual testing	50000	7500000						214	21.70

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T09:46:32

Oliver Kruse

GTX-1

519057529

14549339801

9A67D00458C471__

2017-11-11T22:45:16

ATH

ec2-1xf

519057529

14549339801

9A67D00458C471__

2021-01-21T15:57:25

mrh

lanai

519057529

14549339801

29977306474712467616407

69524E8784162652

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

10¹²

10¹³

10¹⁴

10¹⁵

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