M2062477 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	14.4069	68.6567%	500000	15000000	0.1230	5.1420%	14.5299	70.2684%	1.6117%
PrimeNet	2⁵⁸	0.0186	63.7931%	9000	160000	0.0016	2.6687%	0.0203	64.7594%	0.9662%
GPU72	2⁶²	0.2979	66.1290%	9000	130000	0.0015	1.3653%	0.2994	66.5915%	0.4625%
Difference	+5	+14.1090	+2.5277%	+491000	+14870000	+0.1215	+3.7767%	+14.2305	+3.6769%	+3.6769%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.4069

68.6567%

500000

15000000

0.1230

5.1420%

14.5299

70.2684%

1.6117%

PrimeNet

2⁵⁸

0.0186

63.7931%

9000

160000

0.0016

2.6687%

0.0203

64.7594%

0.9662%

GPU72

2⁶²

0.2979

66.1290%

9000

130000

0.0015

1.3653%

0.2994

66.5915%

0.4625%

Difference

+14.1090

+2.5277%

+491000

+14870000

+0.1215

+3.7767%

+14.2305

+3.6769%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2062477	144373391	9	27.105	35 5 × 7	-	5	7	8.735e-12	4.871e-7	9.701e-7
2062477	23447253689600747999	20	64.346	5684246100587 5684246100587	2017-09-18	1	5684246100587	3.2264	29,525	55,145

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2062477

144373391

27.105

35
5 × 7

8.735e-12

4.871e-7

9.701e-7

2062477

23447253689600747999

64.346

5684246100587
5684246100587

2017-09-18

5684246100587

3.2264

29,525

55,145

exponent	prime factors	composite factor	digits	bits*
2062477	144373391 23447253689600747999	3385159524804921424752094609	28	91.451

exponent

prime factors

composite factor

digits

bits*

2062477

144373391
23447253689600747999

3385159524804921424752094609

91.451

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T13:42:51	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 144373391	-	-	0.123	-	-	5.142%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-09-18T11:06:21	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	23447253689600747999	64.346	20	1.501	0.275	3.047

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.552 GHz-days
Estimated T-Level:	1.700

Digits	B1	Curves	Complete	FacMiss
20	11000	34 / 100	0.340	71.055%
25	50000	34 / 280	0.121	88.546%

New Calculation Method

Total ECM effort:	3.552 GHz-days
Estimated T-Level:	1.700

Digits	B1	Complete	FacMiss
20	11000	1.428	23.980%
25	50000	0.131	87.723%
30	250000	0.008	99.176%

ECM Summary

B1	B2	curves	GHz-days
50000	50000	7	0.355
50000	5000000	6	0.509
50000	5762897	7	0.631
50000	6750000	14	1.358
50000	7150000	7	0.698

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-01T15:58:03	Oliver Kruse	HTC5	50000	5000000						3	0.255
2019-07-25T22:45:25	MarkS	laptop64	50000	5000000						3	0.255
2021-08-09T11:57:05	LordJulius	WhiteBox	50000	6750000						7	0.679
2021-11-11T08:48:48	JackBlock		50000	50000						7	0.355
2021-11-26T04:08:56	happy5214	Focus	50000	6750000						7	0.679
2022-05-04T11:26:10	debrouxl	z400	50000	5762897						7	0.631
2022-07-04T11:46:22	debrouxl	athlon2	50000	7150000						7	0.698

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T11:10:40

Oliver Kruse

GTX-0

144373391

23447253689600747999

D255AF8A9769FE__

2017-11-16T00:44:13

kkmrkkblmbrbk

c4.xlarge

144373391

23447253689600747999

D255AF8A9769FE__

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

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