M1859531 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	15.9793	68.6567%	500000	15000000	0.1015	5.0784%	16.0807	70.2484%	1.5917%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0260%	0.0117	64.2727%	1.1148%
GPU72	2⁶¹	0.1652	65.5738%	9000	150000	0.0013	1.6327%	0.1665	66.1358%	0.5621%
Difference	+6	+15.8141	+3.0829%	+491000	+14850000	+0.1002	+3.4457%	+15.9142	+4.1126%	+4.1126%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9793

68.6567%

500000

15000000

0.1015

5.0784%

16.0807

70.2484%

1.5917%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0260%

0.0117

64.2727%

1.1148%

GPU72

2⁶¹

0.1652

65.5738%

9000

150000

0.0013

1.6327%

0.1665

66.1358%

0.5621%

Difference

+15.8141

+3.0829%

+491000

+14850000

+0.1002

+3.4457%

+15.9142

+4.1126%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1859531	371906201	9	28.470	100 2² × 5²	-	25	25	1.965e-11	1.967e-6	4.002e-6
1859531	1184479057951686746209	22	70.005	318488655997584 2⁴ × 3² × 587 × 3767848003	2020-09-30	587	3767848003	207.66	16.148	30.160
1859531	372068558801276768444983	24	78.300	100043655846898161 3 × 283 × 1787 × 65941270547	2021-07-23	1787	65941270547	35,208	282.61	527.83

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1859531

371906201

28.470

100
2² × 5²

1.965e-11

1.967e-6

4.002e-6

1859531

1184479057951686746209

70.005

318488655997584
2⁴ × 3² × 587 × 3767848003

2020-09-30

587

3767848003

207.66

16.148

30.160

1859531

372068558801276768444983

78.300

100043655846898161
3 × 283 × 1787 × 65941270547

2021-07-23

1787

65941270547

35,208

282.61

527.83

exponent	prime factors	composite factor	digits	bits*
1859531	371906201 1184479057951686746209	440515106606870659324640342009	30	98.475
1859531	371906201 372068558801276768444983	138374604215327956901930305039583	33	106.770
1859531	1184479057951686746209 372068558801276768444983	440707416022378073175979897417299195900319447	45	148.305
1859531	371906201 1184479057951686746209 372068558801276768444983	16390182084540916018057868810083745562764258022019 0847	54	176.775

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:36:49	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 371906201	-	-	0.101	-	-	5.078%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:36:49

alpertron

Manual testing

500000

15000000

skipped known factor: 371906201

0.101

-

-

5.078%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.769 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:	19.769 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.805	0.015%
25	50000	0.798	45.038%
30	250000	0.049	95.186%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		40	2.768
50000	5000000	1184479057951686746209	1	0.069
50000	6600000		200	15.61
50000	6600000	372068558801276768444983	17	1.326

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-17T06:33:09	ATH	ec2-1xe	50000	5000000						3	0.208
2019-01-16T22:30:32	MarkS	laptop64	50000	5000000						3	0.208
2020-06-27T11:20:10	nordi	sweet16	50000	5000000						3	0.208
2020-07-25T00:25:11	Ahmed Azhad	c5.large.az	50000	5000000						3	0.208
2020-09-30T05:35:31	nordi	sweet16	50000	5000000	1184479057951686746209	70.005	1	2	1578520885202581	1	0.069
2020-10-11T22:14:41	nordi	sweet16	50000	5000000						7	0.484
2020-12-12T13:01:58	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-03-16T13:23:44	Kublenz	Medion_E4272	50000	5000000						7	0.484
2021-07-11T01:32:01	MarkS	desktop-i7	50000	5000000						7	0.484
2021-07-23T11:17:58	TJAOI	Manual testing	50000	6600000	372068558801276768444983	78.300	17	2		17	1.326
2021-07-23T11:17:58	TJAOI	Manual testing	50000	6600000						200	15.61

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T08:19:37

Oliver Kruse

GTX-2

371906201

DDF23713F811CC__

2017-11-07T07:02:29

kkmrkkblmbrbk

c4.xlarge

371906201

DDF23713F811CC__

2020-09-30T05:48:46

SRJ2877

371906201

1184479057951686746209

F5DEAADC93C2039E

2021-07-23T18:42:32

GURA LOVE

371906201

1184479057951686746209

372068558801276768444983

F5DEAADC93C2039E

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