M444461 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	unknown	3000000	100000000	0.1415	43.2883%	0.1415	43.2883%	43.2883%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	150000	0.0002	18.3298%	0.0002	61.2067%	8.7067%
GPU72	2⁴⁴	0.0000	56.8182%	8000	240000	0.0004	13.6295%	0.0004	62.7037%	5.8855%
Difference	-44	0.0000	-56.8182%	+2992000	+99760000	+0.1411	+29.6588%	+0.1411	-19.4153%	-19.4153%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

3000000

100000000

0.1415

43.2883%

0.1415

43.2883%

PrimeNet

2⁴⁰

0.0000

52.5000%

4500

150000

0.0002

18.3298%

0.0002

61.2067%

8.7067%

GPU72

2⁴⁴

0.0000

56.8182%

8000

240000

0.0004

13.6295%

0.0004

62.7037%

5.8855%

Difference

-44

0.0000

-56.8182%

+2992000

+99760000

+0.1411

+29.6588%

+0.1411

-19.4153%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
444461	72352156350769	14	46.040	81393144 2³ × 3 × 7 × 17 × 28499	-	17	28499	3.298e-5	2.679e-5	4.953e-5
444461	68334863833915784071	20	65.889	76873858261935 3 × 5 × 7 × 70823 × 10337489	2014-11-26	70823	10337489	19.090	0.0108	0.0180
444461	7696095368865570632557447	25	82.670	8657784787490432943 3 × 10613 × 4362511 × 62331967	2020-07-04	4362511	62331967	3,178,220	0.1284	0.1516

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

444461

72352156350769

46.040

81393144
2³ × 3 × 7 × 17 × 28499

28499

3.298e-5

2.679e-5

4.953e-5

444461

68334863833915784071

65.889

76873858261935
3 × 5 × 7 × 70823 × 10337489

2014-11-26

70823

10337489

19.090

0.0108

0.0180

444461

7696095368865570632557447

82.670

8657784787490432943
3 × 10613 × 4362511 × 62331967

2020-07-04

4362511

62331967

3,178,220

0.1284

0.1516

exponent	prime factors	composite factor	digits	bits*
444461	72352156350769 68334863833915784071	4944174752319984752126112738800599	34	111.929
444461	72352156350769 7696095368865570632557447	556829095418590985877422429517275126743	39	128.711
444461	68334863833915784071 7696095368865570632557447	525911629084258638405360776220735854955026737	45	148.560
444461	72352156350769 68334863833915784071 7696095368865570632557447	38050840414191914372508572452213765126670762566314 745510753	59	194.600

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2014-11-26T19:12:00	alpertron	Manual testing	3000000	100000000	12		68334863833915784071	20	65.889	0.141	0.010	0.283	34.780%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2014-11-26T19:12:00

alpertron

Manual testing

3000000

100000000

68334863833915784071

65.889

0.141

0.010

0.283

34.780%

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.136 GHz-days
Estimated T-Level:	26.398

Digits	B1	Curves	Complete	FacMiss
20	11000	460 / 100	4.600	0.982%
25	50000	460 / 280	1.643	19.286%
30	250000	179 / 640	0.280	75.585%

New Calculation Method

Total ECM effort:	15.136 GHz-days
Estimated T-Level:	26.398

Digits	B1	Complete	FacMiss
20	11000	23.981	0.000%
25	50000	2.976	5.100%
30	250000	0.283	75.336%
35	1000000	0.022	97.856%
40	3000000	0.001	99.862%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	3.617
250000	25000000		144	9.267
250000	25000000	7696095368865570632557447	35	2.252

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-12-26T10:49:00	TJAOI	Manual testing	50000	5000000						50	0.644
2015-04-17T10:32:00	TJAOI	Manual testing	50000	5000000						50	0.644
2016-01-22T16:33:59	TJAOI	Manual testing	50000	5000000						90	1.158
2016-07-22T12:41:07	TJAOI	Manual testing	50000	5000000						91	1.171
2018-03-23T17:14:11	TJAOI	Manual testing	250000	25000000						44	2.832
2020-07-04T21:57:12	nordi	sweet16	250000	25000000	7696095368865570632557447	82.670	35	2	1048983586046649	35	2.252
2020-08-07T11:03:31	TJAOI	Manual testing	250000	25000000						100	6.436

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-24T14:17:43

Oliver Kruse

Doppelherz

72352156350769

68334863833915784071

CCEFAC14543838__

2017-09-24T17:48:08

Oliver Kruse

Manual testing

72352156350769

68334863833915784071

CCEFAC14543838__

2017-11-09T03:13:37

kkmrkkblmbrbk

c4.large

72352156350769

68334863833915784071

CCEFAC14543838__

2020-04-18T19:08:48

Oliver Kruse

AddPrpType5

72352156350769

68334863833915784071

CA97F81F4AAA0E__

2020-07-05T17:56:05

mnd9

mnd

72352156350769

68334863833915784071

7696095368865570632557447

CA97F81F4AAA0E33

2020-07-08T15:47:55

Klaus Nordmann

no1

72352156350769

68334863833915784071

7696095368865570632557447

CA97F81F4AAA0E33

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

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