M1828531 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	16.2502	68.6567%	500000	15000000	0.1015	5.0681%	16.3516	70.2452%	1.5885%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8787%	0.0117	64.2185%	1.0606%
GPU72	2⁶¹	0.1680	65.5738%	9000	140000	0.0013	1.5943%	0.1693	66.1226%	0.5489%
Difference	+6	+16.0822	+3.0829%	+491000	+14860000	+0.1002	+3.4737%	+16.1824	+4.1226%	+4.1226%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.2502

68.6567%

500000

15000000

0.1015

5.0681%

16.3516

70.2452%

1.5885%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8787%

0.0117

64.2185%

1.0606%

GPU72

2⁶¹

0.1680

65.5738%

9000

140000

0.0013

1.5943%

0.1693

66.1226%

0.5489%

Difference

+16.0822

+3.0829%

+491000

+14860000

+0.1002

+3.4737%

+16.1824

+4.1226%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1828531	687527657	9	29.357	188 2² × 47	-	4	47	4.071e-11	4.989e-7	6.404e-7
1828531	912063790789427109758535073	27	89.559	249397956826935695856 2⁴ × 3⁵ × 7² × 11 × 56659 × 2100433637	2020-06-20	56659	2100433637	123,415,564	9.0061	16.813

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1828531

687527657

29.357

188
2² × 47

4.071e-11

4.989e-7

6.404e-7

1828531

912063790789427109758535073

89.559

249397956826935695856
2⁴ × 3⁵ × 7² × 11 × 56659 × 2100433637

2020-06-20

56659

2100433637

123,415,564

9.0061

16.813

exponent	prime factors	composite factor	digits	bits*
1828531	687527657 912063790789427109758535073	627069081115993001144567454492013961	36	118.916

exponent

prime factors

composite factor

digits

bits*

1828531

687527657
912063790789427109758535073

627069081115993001144567454492013961

118.916

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:39:10	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 687527657	-	-	0.101	-	-	5.068%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:39:10

alpertron

Manual testing

500000

15000000

skipped known factor: 687527657

0.101

-

-

5.068%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.820 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:	19.820 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.828	0.015%
25	50000	0.800	44.932%
30	250000	0.049	95.171%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.072
50000	5000000	912063790789427109758535073	1	0.069
50000	6600000		220	17.13
50000	6750000		7	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-09-03T14:58:19	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-06T17:03:13	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-10-24T18:37:35	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-11T13:40:49	kracker	O0	50000	5000000						3	0.207
2020-06-20T05:07:06	nordi	sweet16	50000	5000000	912063790789427109758535073	89.559	1	2	2851891889312364	1	0.069
2020-06-27T06:22:05	nordi	sweet16	50000	5000000						3	0.207
2020-07-24T17:53:09	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-09-29T21:43:37	nordi	sweet16	50000	5000000						7	0.483
2020-11-28T10:46:17	nordi	sweet16	50000	5000000						7	0.483
2021-02-25T05:24:44	Deufo	Ryzen2600	50000	6750000						7	0.551
2021-04-16T16:25:15	TJAOI	Manual testing	50000	6600000						220	17.13

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T01:14:09

Oliver Kruse

GTX-0

687527657

35E2447724B291__

2017-11-06T06:01:24

kkmrkkblmbrbk

c4.xlarge

687527657

35E2447724B291__

2020-06-20T07:14:00

CrypticClue

cruncher

687527657

912063790789427109758535073

7FDEF38E74ABD59F

2020-06-21T05:50:56

marssystems

system03

687527657

912063790789427109758535073

7FDEF38E74ABD59F

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

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