M1939363 Mersenne number exponent details

Residue

Status

L-L

C0AB57B72B4C5401

double-checked

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	15.3215	68.6567%	500000	15000000	0.1015	5.1041%	15.4230	70.2565%	1.5998%
PrimeNet	2⁵⁸	0.0198	63.7931%	8000	140000	0.0012	2.4641%	0.0210	64.6853%	0.8922%
GPU72	2⁶²	0.3168	66.1290%	8000	90000	0.0010	1.1518%	0.3178	66.5191%	0.3901%
Difference	+5	+15.0047	+2.5277%	+492000	+14910000	+0.1005	+3.9524%	+15.1052	+3.7374%	+3.7374%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.3215

68.6567%

500000

15000000

0.1015

5.1041%

15.4230

70.2565%

1.5998%

PrimeNet

2⁵⁸

0.0198

63.7931%

8000

140000

0.0012

2.4641%

0.0210

64.6853%

0.8922%

GPU72

2⁶²

0.3168

66.1290%

8000

90000

0.0010

1.1518%

0.3178

66.5191%

0.3901%

Difference

+15.0047

+2.5277%

+492000

+14910000

+0.1005

+3.9524%

+15.1052

+3.7374%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1939363	55767951314804873279	20	65.596	14377904320853 53 × 74903 × 3621767	2008-11-14	74903	3621767	5.1072	0.0211	0.0290

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1939363

55767951314804873279

65.596

14377904320853
53 × 74903 × 3621767

2008-11-14

74903

3621767

5.1072

0.0211

0.0290

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:41:40	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 55767951314804873279	-	-	0.101	-	-	5.104%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:41:40

alpertron

Manual testing

500000

15000000

skipped known factor: 55767951314804873279

0.101

-

-

5.104%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1998-12-21T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.020

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.191 GHz-days
Estimated T-Level:	24.429

Digits	B1	Curves	Complete	FacMiss
20	11000	248 / 100	2.480	8.270%
25	50000	248 / 280	0.886	41.177%

New Calculation Method

Total ECM effort:	19.191 GHz-days
Estimated T-Level:	24.429

Digits	B1	Complete	FacMiss
20	11000	8.483	0.021%
25	50000	0.769	46.358%
30	250000	0.048	95.355%
35	1000000	0.002	99.781%

ECM Summary

B1	B2	factor	curves	GHz-days
		55767951314804873279	1	0.00000e+0
50000	5000000		31	2.155
50000	6600000		210	16.48
50000	6750000		7	0.555

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-14T16:01:00	Chang Chia-Tche	euler12			55767951314804873279	65.596		1		1	-
2015-04-25T17:55:00	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2015-05-08T13:47:00	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2015-05-20T07:21:00	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2020-11-08T22:36:24	Albrecht Heeffer	Ryzen5-factoring	50000	5000000						7	0.487
2021-02-08T09:44:36	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.487
2021-05-22T16:36:38	Dylan Delgado	laptop-ryzen73700	50000	6750000						7	0.555
2021-09-03T18:49:43	Alvin Bunk	BADCAT	50000	5000000						7	0.487
2021-12-15T07:20:57	MarkS	laptop64	50000	5000000						7	0.487
2022-03-10T10:41:58	TJAOI	Manual testing	50000	6600000						210	16.48

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	ANONYMOUS	v4_computers	C0AB57B72B4C5401	0.105

date

userid

compid

res64

spent (GHz-days)

1999-01-02T00:00:00

ANONYMOUS

v4_computers

C0AB57B72B4C5401

0.105

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)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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