M2073853 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	14.3279	68.6567%	500000	15000000	0.1230	5.1454%	14.4509	70.2695%	1.6127%
PrimeNet	2⁵⁸	0.0185	63.7931%	9000	160000	0.0016	2.6714%	0.0202	64.7604%	0.9672%
GPU72	2⁶²	0.2962	66.1290%	9000	130000	0.0015	1.3669%	0.2977	66.5920%	0.4630%
Difference	+5	+14.0316	+2.5277%	+491000	+14870000	+0.1215	+3.7785%	+14.1531	+3.6775%	+3.6775%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.3279

68.6567%

500000

15000000

0.1230

5.1454%

14.4509

70.2695%

1.6127%

PrimeNet

2⁵⁸

0.0185

63.7931%

9000

160000

0.0016

2.6714%

0.0202

64.7604%

0.9672%

GPU72

2⁶²

0.2962

66.1290%

9000

130000

0.0015

1.3669%

0.2977

66.5920%

0.4630%

Difference

+14.0316

+2.5277%

+491000

+14870000

+0.1215

+3.7785%

+14.1531

+3.6775%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2073853	8656262423	10	33.011	2087 2087	-	1	2087	8.011e-10	1.093e-5	2.022e-5
2073853	683066455784161	15	49.279	164685360 2⁴ × 3 × 5 × 7 × 61 × 1607	2008-09-30	61	1607	4.274e-5	1.385e-5	1.556e-5
2073853	9591520632262863934033	22	73.022	2312488067443272 2³ × 3² × 19 × 71 × 23808665549	2019-08-09	71	23808665549	1,511.8	123.67	230.98

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2073853

8656262423

33.011

2087
2087

2087

8.011e-10

1.093e-5

2.022e-5

2073853

683066455784161

49.279

164685360
2⁴ × 3 × 5 × 7 × 61 × 1607

2008-09-30

1607

4.274e-5

1.385e-5

1.556e-5

2073853

9591520632262863934033

73.022

2312488067443272
2³ × 3² × 19 × 71 × 23808665549

2019-08-09

23808665549

1,511.8

123.67

230.98

exponent	prime factors	composite factor	digits	bits*
2073853	8656262423 683066455784161	5912802493616223862882103	25	82.290
2073853	8656262423 9591520632262863934033	83026719628486230530531808741959	32	106.033
2073853	683066455784161 9591520632262863934033	6551646003860449506083154808390251313	37	122.301
2073853	8656262423 683066455784161 9591520632262863934033	56712767112015321995396522881160297560248311399	47	155.312

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T13:44:13	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 8656262423 skipped known factor: 683066455784161	-	-	0.123	-	-	5.145%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:36:00	markr	Manual testing	?	?	683066455784161	49.279	15	6.57496e-6	0.295	1.42388e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.545 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	2.545 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	0.938	39.148%
25	50000	0.085	91.849%
30	250000	0.005	99.476%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		10	0.850
50000	5000000	9591520632262863934033	3	0.255
50000	6364613		7	0.661
50000	6750000		7	0.679
50000	7150000		1	0.100

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-03T07:12:20	Oliver Kruse	ECM-HTC	50000	5000000						3	0.255
2019-08-09T21:24:55	MarkS	laptop64	50000	5000000	9591520632262863934033	73.022	3	2		3	0.255
2021-08-27T12:43:25	happy5214	Focus	50000	6750000						7	0.679
2021-12-16T18:50:13	-Anonymous-	UMA2022	50000	7150000						1	0.100
2022-01-17T07:29:06	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.595
2022-05-18T05:43:22	debrouxl	o9020	50000	6364613						7	0.661

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T14:44:54

Oliver Kruse

GTX-1

8656262423

683066455784161

3E48DDF51D7E66__

2017-11-16T09:10:46

kkmrkkblmbrbk

c4.xlarge

8656262423

683066455784161

3E48DDF51D7E66__

2019-08-10T10:55:16

trebor

Laptop

8656262423

683066455784161

9591520632262863934033

2ED0B5DF7A9C80B4

2019-08-12T02:18:46

arnaud

stm-11-010

8656262423

683066455784161

9591520632262863934033

2ED0B5DF7A9C80B4

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

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