M1970219 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	15.0815	68.6567%	-	-	-	-	15.0815	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0014	2.4717%	0.0209	64.6880%	0.8949%
GPU72	2⁶²	0.3118	66.1290%	8000	100000	0.0012	1.1959%	0.3131	66.5341%	0.4051%
Difference	+5	+14.7697	+2.5277%	-8000	-100000	-0.0012	-1.1959%	+14.7685	+2.1226%	+2.1226%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.0815

68.6567%

15.0815

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0014

2.4717%

0.0209

64.6880%

0.8949%

GPU72

2⁶²

0.3118

66.1290%

8000

100000

0.0012

1.1959%

0.3131

66.5341%

0.4051%

Difference

+14.7697

+2.5277%

-8000

-100000

-0.0012

-1.1959%

+14.7685

+2.1226%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1970219	3940439	7	21.910	1 1	-	1	1	1.418e-13	9.534e-8	1.940e-7
1970219	384777544807961	15	48.451	97648420 2² × 5 × 4882421	2014-04-04	5	4882421	1.944e-5	0.0254	0.0474

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1970219

3940439

21.910

1
1

1.418e-13

9.534e-8

1.940e-7

1970219

384777544807961

48.451

97648420
2² × 5 × 4882421

2014-04-04

4882421

1.944e-5

0.0254

0.0474

exponent	prime factors	composite factor	digits	bits*
1970219	3940439 384777544807961	1516192443885537034879	22	70.361

exponent

prime factors

composite factor

digits

bits*

1970219

3940439
384777544807961

1516192443885537034879

70.361

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-04-04T10:34:00	TJAOI	Manual testing	?	?	384777544807961	48.451	15	4.11952e-7	0.283	8.98926e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.712 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	3.712 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.644	19.316%
25	50000	0.152	85.904%
30	250000	0.010	99.041%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.689
50000	6750000		21	2.023

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-21T21:27:54	alpertron	laptop2	50000	5000000						3	0.253
2019-03-27T04:20:30	MarkS	laptop64	50000	5000000						3	0.253
2021-01-24T20:23:16	Kublenz	Medion_E4272	50000	5000000						7	0.591
2021-05-04T09:45:50	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.591
2021-08-11T13:54:45	Dylan Delgado	colab	50000	6750000						7	0.674
2021-11-16T11:57:07	LordJulius	surface7	50000	6750000						7	0.674
2022-04-19T02:53:01	Dylan Delgado	colab	50000	6750000						7	0.674

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T10:29:59

Oliver Kruse

GTX-3

3940439

384777544807961

9D0119E92D8B26__

2017-11-12T03:18:32

kkmrkkblmbrbk

c4.xlarge

3940439

384777544807961

9D0119E92D8B26__

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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