M1812793 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	16.3912	68.6567%	500000	15000000	0.1015	5.0628%	16.4927	70.2436%	1.5869%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8740%	0.0118	64.2167%	1.0588%
GPU72	2⁶¹	0.1695	65.5738%	9000	130000	0.0012	1.5566%	0.1707	66.1097%	0.5359%
Difference	+6	+16.2218	+3.0829%	+491000	+14870000	+0.1002	+3.5062%	+16.3220	+4.1339%	+4.1339%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3912

68.6567%

500000

15000000

0.1015

5.0628%

16.4927

70.2436%

1.5869%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8740%

0.0118

64.2167%

1.0588%

GPU72

2⁶¹

0.1695

65.5738%

9000

130000

0.0012

1.5566%

0.1707

66.1097%

0.5359%

Difference

+16.2218

+3.0829%

+491000

+14870000

+0.1002

+3.5062%

+16.3220

+4.1339%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1812793	609098449	9	29.182	168 2³ × 3 × 7	-	8	8	4.089e-11	6.293e-7	1.281e-6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1812793

609098449

29.182

168
2³ × 3 × 7

4.089e-11

6.293e-7

1.281e-6

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:14	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 609098449	-	-	0.101	-	-	5.063%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:14

alpertron

Manual testing

500000

15000000

skipped known factor: 609098449

0.101

-

-

5.063%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.594 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.594 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.622	0.002%
25	50000	0.974	37.742%
30	250000	0.062	94.007%
35	1000000	0.003	99.710%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		40	2.760
50000	6500000		218	16.83

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-12T21:34:45	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-01T03:43:31	alpertron		50000	5000000						3	0.207
2018-09-28T16:57:36	alpertron	Manual testing	50000	5000000						3	0.207
2020-04-29T22:17:20	Greg	azure4	50000	5000000						3	0.207
2020-05-19T02:45:23	MarkS	desktop-i7	50000	5000000						3	0.207
2020-06-23T03:21:30	kracker	O0	50000	5000000						3	0.207
2020-07-20T10:30:05	-Anonymous-	aws-nano	50000	5000000						3	0.207
2020-09-18T21:46:03	MarkS	desktop-i7	50000	5000000						7	0.483
2020-11-23T07:23:27	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.483
2021-02-19T09:12:48	Chang Chia-Tche	exbpc13	50000	5000000						7	0.483
2021-03-05T18:08:49	TJAOI	Manual testing	50000	6500000						218	16.83

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

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