M1813121 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	16.3883	68.6567%	500000	15000000	0.1015	5.0629%	16.4897	70.2436%	1.5869%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8741%	0.0118	64.2168%	1.0589%
GPU72	2⁶¹	0.1694	65.5738%	9000	130000	0.0012	1.5567%	0.1706	66.1097%	0.5359%
Difference	+6	+16.2188	+3.0829%	+491000	+14870000	+0.1002	+3.5062%	+16.3191	+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

16.3883

68.6567%

500000

15000000

0.1015

5.0629%

16.4897

70.2436%

1.5869%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8741%

0.0118

64.2168%

1.0589%

GPU72

2⁶¹

0.1694

65.5738%

9000

130000

0.0012

1.5567%

0.1706

66.1097%

0.5359%

Difference

+16.2188

+3.0829%

+491000

+14870000

+0.1002

+3.5062%

+16.3191

+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
1813121	16013484673	11	33.899	4416 2⁶ × 3 × 23	-	64	64	1.234e-9	5.034e-6	1.025e-5
1813121	3956203970233834382259894601	28	91.676	1090992815767352091300 2² × 3 × 5² × 7 × 17 × 19 × 2729 × 589381551959	2020-05-24	2729	589381551959	452,598,154	2,525.9	4,717.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1813121

16013484673

33.899

4416
2⁶ × 3 × 23

1.234e-9

5.034e-6

1.025e-5

1813121

3956203970233834382259894601

91.676

1090992815767352091300
2² × 3 × 5² × 7 × 17 × 19 × 2729 × 589381551959

2020-05-24

2729

589381551959

452,598,154

2,525.9

4,717.8

exponent	prime factors	composite factor	digits	bits*
1813121	16013484673 3956203970233834382259894601	63352611640601255106339245295708950473	38	125.575

exponent

prime factors

composite factor

digits

bits*

1813121

16013484673
3956203970233834382259894601

63352611640601255106339245295708950473

125.575

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:37:15	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 16013484673	-	-	0.101	-	-	5.063%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.318 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.318 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		207	14.28
50000	5000000	3956203970233834382259894601	44	3.036

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-18T11:10:17	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-01T08:50:02	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-09-28T21:07:50	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-04-30T02:38:27	Greg	azure4	50000	5000000						3	0.207
2020-05-24T10:32:38	nordi	sweet16	50000	5000000	3956203970233834382259894601	91.676	44	2	5582382914025906	44	3.036
2021-02-19T17:09:58	TJAOI	Manual testing	50000	5000000						197	13.59

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T21:34:40

Oliver Kruse

GTX-1

16013484673

F310FC0C9158AF__

2017-11-05T19:32:24

kkmrkkblmbrbk

c4.xlarge

16013484673

F310FC0C9158AF__

2020-05-24T12:35:06

CrypticClue

cruncher

16013484673

3956203970233834382259894601

9DFB720B84310584

2020-05-25T10:58:10

marssystems

system03

16013484673

3956203970233834382259894601

9DFB720B84310584

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

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