M1862611 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	15.9528	68.6567%	500000	15000000	0.1015	5.0794%	16.0543	70.2488%	1.5920%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0269%	0.0117	64.2731%	1.1152%
GPU72	2⁶¹	0.1649	65.5738%	10000	150000	0.0014	1.6883%	0.1663	66.1550%	0.5812%
Difference	+6	+15.7879	+3.0829%	+490000	+14850000	+0.1001	+3.3911%	+15.8880	+4.0938%	+4.0938%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9528

68.6567%

500000

15000000

0.1015

5.0794%

16.0543

70.2488%

1.5920%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0269%

0.0117

64.2731%

1.1152%

GPU72

2⁶¹

0.1649

65.5738%

10000

150000

0.0014

1.6883%

0.1663

66.1550%

0.5812%

Difference

+15.7879

+3.0829%

+490000

+14850000

+0.1001

+3.3911%

+15.8880

+4.0938%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1862611	1191981634673	13	40.116	319976 2³ × 23 × 37 × 47	-	37	47	9.900e-8	2.953e-6	5.923e-6
1862611	355815823975157689553	21	68.270	95515334113016 2³ × 37 × 322686939571	2020-07-28	37	322686939571	34.474	1,383.0	2,583.0
1862611	25057359245814153320999	23	74.408	6726406975427009 13 × 517415921186693	2020-12-03	13	517415921186693	2,920.6	2,217,515	4,141,701

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1862611

1191981634673

40.116

319976
2³ × 23 × 37 × 47

9.900e-8

2.953e-6

5.923e-6

1862611

355815823975157689553

68.270

95515334113016
2³ × 37 × 322686939571

2020-07-28

322686939571

34.474

1,383.0

2,583.0

1862611

25057359245814153320999

74.408

6726406975427009
13 × 517415921186693

2020-12-03

517415921186693

2,920.6

2,217,515

4,141,701

exponent	prime factors	composite factor	digits	bits*
1862611	1191981634673 355815823975157689553	424125927504428887736330794671169	33	108.386
1862611	1191981634673 25057359245814153320999	29867912034414164908323839717398327	35	114.524
1862611	355815823975157689553 25057359245814153320999	8915804926690898817407074706109286797823447	43	142.677
1862611	1191981634673 355815823975157689553 25057359245814153320999	10627475730942604500964527455463178737055770013507 577831	56	182.794

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:12	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1191981634673	-	-	0.101	-	-	5.079%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:12

alpertron

Manual testing

500000

15000000

skipped known factor: 1191981634673

0.101

-

-

5.079%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.346 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	20.346 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	9.053	0.012%
25	50000	0.820	44.036%
30	250000	0.051	95.053%
35	1000000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.076
50000	5000000	355815823975157689553	3	0.208
50000	5000000	25057359245814153320999	5	0.346
50000	6600000		227	17.72

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T12:40:54	Oliver Kruse	ECM-HTC	50000	5000000						3	0.208
2019-01-17T18:05:05	tottenhoff	i7-8700k-01	50000	5000000						3	0.208
2020-07-01T04:45:32	LaurV	3tits	50000	5000000						3	0.208
2020-07-28T01:06:10	-Anonymous-	aws-nano	50000	5000000	355815823975157689553	68.270	3	2	5159142710826754	3	0.208
2020-10-06T22:18:26	nordi	sweet16	50000	5000000						7	0.484
2020-12-03T04:45:31	MarkS	desktop-i7	50000	5000000	25057359245814153320999	74.408	5	2	4287767487684081	5	0.346
2021-04-05T22:11:25	Chang Chia-Tche	exbpc13	50000	5000000						7	0.484
2021-05-22T22:06:54	Chang Chia-Tche	exbpc13	50000	5000000						7	0.484
2021-08-13T08:33:18	TJAOI	Manual testing	50000	6600000						227	17.72

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T09:13:31

Oliver Kruse

GTX-0

1191981634673

CF6990D3C989C5__

2017-11-07T09:07:36

kkmrkkblmbrbk

c4.xlarge

1191981634673

CF6990D3C989C5__

2020-07-28T03:24:36

CrypticClue

cruncher

1191981634673

355815823975157689553

2C7F80B8B187390C

2020-08-01T15:17:13

nordi

sweet16

1191981634673

355815823975157689553

2C7F80B8B187390C

2020-12-04T03:43:51

Yuji HASEGAWA

vj20a

1191981634673

355815823975157689553

25057359245814153320999

2C7F80B8B187390C

2020-12-04T09:42:01

Jinyuan Wang

Manual testing

1191981634673

355815823975157689553

25057359245814153320999

2C7F80B8B187390C

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

10¹³

10¹⁴

10¹⁵

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