M1926359 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	15.4249	68.6567%	500000	15000000	0.1015	5.1000%	15.5264	70.2552%	1.5985%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0947%	0.0114	64.2980%	1.1402%
GPU72	2⁶¹	0.1595	65.5738%	11000	170000	0.0015	1.8141%	0.1610	66.1983%	0.6245%
Difference	+6	+15.2655	+3.0829%	+489000	+14830000	+0.0999	+3.2859%	+15.3654	+4.0569%	+4.0569%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.4249

68.6567%

500000

15000000

0.1015

5.1000%

15.5264

70.2552%

1.5985%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0947%

0.0114

64.2980%

1.1402%

GPU72

2⁶¹

0.1595

65.5738%

11000

170000

0.0015

1.8141%

0.1610

66.1983%

0.6245%

Difference

+15.2655

+3.0829%

+489000

+14830000

+0.0999

+3.2859%

+15.3654

+4.0569%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1926359	34674463	8	25.047	9 3²	-	9	9	2.325e-12	7.080e-7	1.441e-6
1926359	97731670195639	14	46.474	25366941 3² × 17 × 37 × 4481	2014-02-13	37	4481	8.175e-6	2.196e-5	3.586e-5
1926359	10304125824114542161785103	26	83.091	2674508184641217489 3 × 59 × 15110215732436257	2020-11-02	59	15110215732436257	2,022,594	64,758,607	120,951,044

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1926359

34674463

25.047

9
3²

2.325e-12

7.080e-7

1.441e-6

1926359

97731670195639

46.474

25366941
3² × 17 × 37 × 4481

2014-02-13

4481

8.175e-6

2.196e-5

3.586e-5

1926359

10304125824114542161785103

83.091

2674508184641217489
3 × 59 × 15110215732436257

2020-11-02

15110215732436257

2,022,594

64,758,607

120,951,044

exponent	prime factors	composite factor	digits	bits*
1926359	34674463 97731670195639	3388793182126887266857	22	71.521
1926359	34674463 10304125824114542161785103	357290029635604199950757567924689	33	108.139
1926359	97731670195639 10304125824114542161785103	1007039426696729348860613211301485765817	40	129.565
1926359	34674463 97731670195639 10304125824114542161785103	34918551340536954028081424952584550031848231271	47	154.613

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:19:05	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 34674463 skipped known factor: 97731670195639	-	-	0.101	-	-	5.100%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-02-13T14:29:00	TJAOI	Manual testing	?	?	97731670195639	46.474	14	3.30851e-6	0.223	7.04717e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-02-13T14:29:00

TJAOI

Manual testing

97731670195639

46.474

3.30851e-6

0.223

7.04717e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.135 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.135 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.519	0.020%
25	50000	0.772	46.228%
30	250000	0.048	95.341%
35	1000000	0.002	99.781%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		59	4.099
50000	5000000	10304125824114542161785103	2	0.139
50000	6600000		190	14.90

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-20T07:06:21	Oliver Kruse	ECM-HTC	50000	5000000						3	0.208
2019-02-05T22:01:11	ATH	ec2-ECMCF	50000	5000000						3	0.208
2020-11-02T14:51:14	nordi	sweet16	50000	5000000	10304125824114542161785103	83.091	2	2	2243615358282605	2	0.139
2020-11-24T06:52:21	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-02-20T22:17:19	MarkS	desktop-i7	50000	5000000						7	0.486
2021-06-11T13:29:13	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2021-09-09T23:06:19	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486
2021-12-26T00:04:00	MarkS	desktop-i7	50000	5000000						25	1.737
2022-03-10T10:40:47	TJAOI	Manual testing	50000	6600000						190	14.90

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T23:53:02

Oliver Kruse

GTX-1

34674463

97731670195639

AF83BD373A132D__

2017-11-10T07:01:14

ATH

ec2-1xf

34674463

97731670195639

AF83BD373A132D__

2020-11-02T16:06:31

Oliver Kruse

IOS-5

34674463

97731670195639

10304125824114542161785103

1E6EF1F2CD658C__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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