M1872547 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	15.8682	68.6567%	500000	15000000	0.1015	5.0826%	15.9697	70.2498%	1.5931%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0299%	0.0116	64.2742%	1.1163%
GPU72	2⁶¹	0.1640	65.5738%	10000	150000	0.0014	1.6901%	0.1654	66.1556%	0.5818%
Difference	+6	+15.7041	+3.0829%	+490000	+14850000	+0.1001	+3.3925%	+15.8042	+4.0942%	+4.0942%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.8682

68.6567%

500000

15000000

0.1015

5.0826%

15.9697

70.2498%

1.5931%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0299%

0.0116

64.2742%

1.1163%

GPU72

2⁶¹

0.1640

65.5738%

10000

150000

0.0014

1.6901%

0.1654

66.1556%

0.5818%

Difference

+15.7041

+3.0829%

+490000

+14850000

+0.1001

+3.3925%

+15.8042

+4.0942%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1872547	2041720011658601	16	50.859	545171900 2² × 5² × 7 × 13 × 139 × 431	-	139	431	0.0001	1.219e-5	2.225e-5
1872547	72192306169165386119	20	65.968	19276500448097 19 × 1014552655163	2018-04-15	19	1014552655163	5.4656	4,348.1	8,121.1
1872547	511812748135906161169817	24	78.760	136662190090797764 2² × 31 × 211 × 283 × 13681 × 1349087	2015-08-17	13681	1349087	58,902	0.0068	0.0108

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1872547

2041720011658601

50.859

545171900
2² × 5² × 7 × 13 × 139 × 431

139

431

0.0001

1.219e-5

2.225e-5

1872547

72192306169165386119

65.968

19276500448097
19 × 1014552655163

2018-04-15

1014552655163

5.4656

4,348.1

8,121.1

1872547

511812748135906161169817

78.760

136662190090797764
2² × 31 × 211 × 283 × 13681 × 1349087

2015-08-17

13681

1349087

58,902

0.0068

0.0108

exponent	prime factors	composite factor	digits	bits*
1872547	2041720011658601 72192306169165386119	147396476193369645043022419772359519	36	116.827
1872547	2041720011658601 511812748135906161169817	1044978330091062944613662471760589646017	40	129.619
1872547	72192306169165386119 511812748135906161169817	36948942614709268333493810070245137533570223	44	144.728
1872547	2041720011658601 72192306169165386119 511812748135906161169817	75439395546077186658653072398760169783811026397579 335438023	59	195.587

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-08-17T12:52:00	alpertron	Manual testing	500000	15000000	12		511812748135906161169817	24	78.760	0.101	0.203	0.203	5.083%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-08-17T12:52:00

alpertron

Manual testing

500000

15000000

511812748135906161169817

78.760

0.101

0.203

0.203

5.083%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.258 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:	19.258 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.568	0.019%
25	50000	0.776	46.015%
30	250000	0.048	95.312%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		38	2.631
50000	5000000	72192306169165386119	1	0.069
50000	6600000		212	16.56

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-05-15T10:05:12	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-15T13:38:33	Chang Chia-Tche	exbpc13	50000	5000000	72192306169165386119	65.968	1	2		1	0.069
2018-11-08T03:30:50	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2020-07-05T16:43:01	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2020-08-06T23:44:46	Ahmed Azhad	c5.xlarge.az	50000	5000000						3	0.208
2020-10-16T14:18:10	J.R. Allen	lapacer	50000	5000000						7	0.485
2020-12-23T16:18:03	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-03-18T21:31:56	Chang Chia-Tche	exbpc13	50000	5000000						7	0.485
2021-07-11T16:33:57	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.485
2021-09-10T07:34:27	TJAOI	Manual testing	50000	6600000						212	16.56

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:53

alpertron

Manual testing

2041720011658601

511812748135906161169817

8F3EFB95D22A92__

2017-10-20T01:48:42

Oliver Kruse

Threadripper

2041720011658601

511812748135906161169817

8F3EFB95D22A92__

2018-04-17T16:33:00

Oliver Kruse

GTX-2

2041720011658601

72192306169165386119

511812748135906161169817

368DCFC82BFFC6__

2018-04-19T00:57:23

Battlemaxx

Work-2

2041720011658601

72192306169165386119

511812748135906161169817

368DCFC82BFFC6__

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

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