M440047 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	67.5244	71.6418%	3000000	100000000	0.1415	7.1845%	67.6659	73.6792%	2.0374%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	140000	0.0002	18.1147%	0.0002	61.1045%	8.6045%
GPU72	2⁴⁴	0.0000	56.8182%	8000	240000	0.0004	13.6120%	0.0004	62.6961%	5.8779%
Difference	+23	+67.5244	+14.8236%	+2992000	+99760000	+0.1411	-6.4275%	+67.6655	+10.9831%	+10.9831%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

67.5244

71.6418%

3000000

100000000

0.1415

7.1845%

67.6659

73.6792%

2.0374%

PrimeNet

2⁴⁰

0.0000

52.5000%

4500

140000

0.0002

18.1147%

0.0002

61.1045%

8.6045%

GPU72

2⁴⁴

0.0000

56.8182%

8000

240000

0.0004

13.6120%

0.0004

62.6961%

5.8779%

Difference

+23

+67.5244

+14.8236%

+2992000

+99760000

+0.1411

-6.4275%

+67.6655

+10.9831%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
440047	1730711977554124249	19	60.586	1966508097492 2² × 3 × 2141 × 76541651	2007-09-04	2141	76541651	0.4723	0.0713	0.1330
440047	1041506016639286615975777	25	79.785	1183403155389409104 2⁴ × 3 × 181 × 683 × 409397 × 487133	2014-11-21	409397	487133	482,020	0.0071	0.0142

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

440047

1730711977554124249

60.586

1966508097492
2² × 3 × 2141 × 76541651

2007-09-04

2141

76541651

0.4723

0.0713

0.1330

440047

1041506016639286615975777

79.785

1183403155389409104
2⁴ × 3 × 181 × 683 × 409397 × 487133

2014-11-21

409397

487133

482,020

0.0071

0.0142

exponent	prime factors	composite factor	digits	bits*
440047	1730711977554124249 1041506016639286615975777	1802546937692298374304302995754457832316473	43	140.371

exponent

prime factors

composite factor

digits

bits*

440047

1730711977554124249
1041506016639286615975777

1802546937692298374304302995754457832316473

140.371

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-01T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.002	-	-	1.476%
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.718%
2002-08-31T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.007	-	-	2.445%
2003-04-03T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.014	-	-	3.300%
2014-11-21T15:50:00	alpertron	Manual testing	3000000	100000000	12		1041506016639286615975777	25	79.785	0.051	0.010	0.102	7.185%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-03-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.022	-	-
2002-02-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.044	-	-
2004-01-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.087	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.877 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	425 / 100	4.250	1.396%
25	50000	425 / 280	1.518	21.859%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	12.877 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		1730711977554124249	1	0.00000e+0
50000	5000000		281	3.615
250000	25000000		144	9.262

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-16T03:06:00	drew	messier	50000	5000000						1	0.013
2007-09-04T15:18:00	Chad Davis	Bayes			1730711977554124249	60.586		1		1	-
2013-12-07T19:37:00	Richard B. Woods	Puttputt	50000	5000000						9	0.116
2015-01-02T14:33:00	TJAOI	Manual testing	50000	5000000						40	0.515
2015-04-03T14:25:00	TJAOI	Manual testing	50000	5000000						50	0.643
2015-04-24T10:38:00	TJAOI	Manual testing	50000	5000000						50	0.643
2016-01-15T14:49:01	TJAOI	Manual testing	50000	5000000						40	0.515
2016-04-15T10:23:39	TJAOI	Manual testing	50000	5000000						91	1.171
2017-12-08T13:27:12	TJAOI	Manual testing	250000	25000000						44	2.830
2020-03-16T11:25:16	TJAOI	Manual testing	250000	25000000						100	6.432

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-24T08:17:57

Oliver Kruse

Doppelherz

1730711977554124249

1041506016639286615975777

74D0DF487B9EAA25

2017-09-24T17:47:50

Oliver Kruse

Manual testing

1730711977554124249

1041506016639286615975777

74D0DF487B9EAA25

2017-10-13T09:26:35

kkmrkkblmbrbk

c4.xlarge

74D0DF487B9EAA__

2020-04-18T18:32:36

Oliver Kruse

AddPrpType5

1730711977554124249

1041506016639286615975777

718CEDC5AAC0F1__

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)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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