M1868387 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	15.9035	68.6567%	5000000	515000000	2.5790	10.8017%	18.4826	72.0423%	3.3856%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0286%	0.0116	64.2737%	1.1158%
GPU72	2⁶¹	0.1644	65.5738%	10000	150000	0.0014	1.6893%	0.1658	66.1553%	0.5816%
Difference	+6	+15.7391	+3.0829%	+4990000	+514850000	+2.5777	+9.1124%	+18.3168	+5.8870%	+5.8870%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9035

68.6567%

5000000

515000000

2.5790

10.8017%

18.4826

72.0423%

3.3856%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0286%

0.0116

64.2737%

1.1158%

GPU72

2⁶¹

0.1644

65.5738%

10000

150000

0.0014

1.6893%

0.1658

66.1553%

0.5816%

Difference

+15.7391

+3.0829%

+4990000

+514850000

+2.5777

+9.1124%

+18.3168

+5.8870%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1868387	47921710426667081	17	55.412	12824353420 2² × 5 × 31 × 67 × 308723	-	67	308723	0.0028	0.0013	0.0025
1868387	1925487808964058219400823	25	80.671	515280776671015753 10429 × 49408454949757	2021-03-28	10429	49408454949757	131,427	211,752	395,494

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1868387

47921710426667081

55.412

12824353420
2² × 5 × 31 × 67 × 308723

308723

0.0028

0.0013

0.0025

1868387

1925487808964058219400823

80.671

515280776671015753
10429 × 49408454949757

2021-03-28

10429

49408454949757

131,427

211,752

395,494

exponent	prime factors	composite factor	digits	bits*
1868387	47921710426667081 1925487808964058219400823	92272669211253261365022967953136718407663	41	136.083

exponent

prime factors

composite factor

digits

bits*

1868387

47921710426667081
1925487808964058219400823

92272669211253261365022967953136718407663

136.083

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:37:45	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 47921710426667081	-	-	0.101	-	-	5.081%
2021-06-08T11:20:49	happy5214	Manual testing	5000000	515000000		-	skipped known factor: 47921710426667081	-	-	2.579	-	-	10.802%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-06-08T11:20:49	happy5214	Manual testing	2500000	195000000	2	7			-	-	1.107

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-06-08T11:20:49

happy5214

Manual testing

2500000

195000000

1.107

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.664 GHz-days
Estimated T-Level:	23.661

Digits	B1	Curves	Complete	FacMiss
20	11000	205 / 100	2.050	12.741%
25	50000	205 / 280	0.732	48.025%

New Calculation Method

Total ECM effort:	15.664 GHz-days
Estimated T-Level:	23.661

Digits	B1	Complete	FacMiss
20	11000	6.984	0.093%
25	50000	0.632	53.130%
30	250000	0.039	96.164%
35	1000000	0.002	99.820%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4850000		7	0.479
50000	5000000		26	1.800
50000	5000000	1925487808964058219400823	5	0.346
50000	6600000		167	13.04

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T16:49:48	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2019-01-19T22:03:52	tottenhoff	2018pc	50000	5000000						3	0.208
2020-07-11T03:50:14	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.208
2020-08-13T04:30:21	volki	home	50000	5000000						3	0.208
2020-10-16T09:45:27	nordi	sweet16	50000	5000000						7	0.485
2020-12-29T23:21:32	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-03-28T12:35:42	Chang Chia-Tche	exbpc13	50000	5000000	1925487808964058219400823	80.671	5	2	5083187339905575	5	0.346
2021-06-29T09:27:43	happy5214	Cosmic	50000	4850000						7	0.479
2021-09-10T07:33:42	TJAOI	Manual testing	50000	6600000						167	13.04

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T10:44:04

Oliver Kruse

GTX-0

47921710426667081

84B79B042A8D68__

2017-11-07T13:39:47

kkmrkkblmbrbk

c4.xlarge

47921710426667081

84B79B042A8D68__

2021-03-30T11:08:23

Oliver Kruse

Threadripper-PC

47921710426667081

1925487808964058219400823

672B2513AD773A3F

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 = 5000000, B2 = 515000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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