M1460021 Mersenne number exponent details

Residue

Status

L-L

EA1920A0F16D7D70

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	20.3517	68.6567%	1000000	30000000	0.1428	6.0375%	20.4945	70.5491%	1.8924%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9080%	0.0073	63.5905%	1.0905%
GPU72	2⁶⁰	0.1052	65.0000%	6500	90000	0.0006	1.3985%	0.1058	65.4895%	0.4895%
Difference	+7	+20.2465	+3.6567%	+993500	+29910000	+0.1422	+4.6390%	+20.3887	+5.0596%	+5.0596%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.3517

68.6567%

1000000

30000000

0.1428

6.0375%

20.4945

70.5491%

1.8924%

PrimeNet

2⁵⁶

0.0066

62.5000%

7000

120000

0.0007

2.9080%

0.0073

63.5905%

1.0905%

GPU72

2⁶⁰

0.1052

65.0000%

6500

90000

0.0006

1.3985%

0.1058

65.4895%

0.4895%

Difference

+20.2465

+3.6567%

+993500

+29910000

+0.1422

+4.6390%

+20.3887

+5.0596%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1460021	1076340200777320226873639	25	79.832	368604355956976039 17 × 373 × 89867 × 646848337	2013-09-11	89867	646848337	91,825	1.9558	3.6440

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1460021

1076340200777320226873639

79.832

368604355956976039
17 × 373 × 89867 × 646848337

2013-09-11

89867

646848337

91,825

1.9558

3.6440

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.840%
2008-12-27T18:27:00	axn	Manual testing	1000000	30000000		-		-	-	0.143	-	-	6.038%
2016-03-17T19:14:37	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.932%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2010-04-15T16:04:00	Richard B. Woods	Puttputt	2⁶⁰	2⁶¹		-	-	0.105	-	-
2011-04-05T20:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.093	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.422 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	298 / 100	2.980	5.004%
25	50000	298 / 280	1.064	34.432%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.422 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.167	0.001%
25	50000	1.348	25.975%
30	250000	0.112	89.363%
35	1000000	0.008	99.239%

ECM Summary

B1	B2	factor	curves	GHz-days
		1076340200777320226873639	1	0.00000e+0
50000	5000000		248	11.75
250000	35000000		50	13.67

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-06T05:30:00	Steve Scott	Abit	50000	5000000						1	0.047
2009-01-16T04:35:00	bladerunner	Nebuchadnezzar	50000	5000000						3	0.142
2009-09-29T11:12:00	JimBa	E5400	50000	5000000						3	0.142
2010-04-26T02:32:00	SubPrime	stor	50000	5000000						3	0.142
2011-07-29T08:25:00	S36049	Wolle5	50000	5000000						3	0.142
2012-11-25T06:43:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.142
2013-09-11T02:52:00	Chang Chia-Tche	exbpc13			1076340200777320226873639	79.832		1		1	-
2019-03-15T12:31:56	TJAOI	Manual testing	50000	5000000						232	11.00
2021-12-28T11:13:26	TJAOI	Manual testing	250000	35000000						50	13.67

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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