M1855697 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	16.0123	68.6567%	500000	15000000	0.1015	5.0771%	16.1137	70.2480%	1.5913%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0248%	0.0117	64.2723%	1.1144%
GPU72	2⁶¹	0.1655	65.5738%	9000	150000	0.0013	1.6320%	0.1668	66.1356%	0.5618%
Difference	+6	+15.8467	+3.0829%	+491000	+14850000	+0.1002	+3.4451%	+15.9469	+4.1124%	+4.1124%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0123

68.6567%

500000

15000000

0.1015

5.0771%

16.1137

70.2480%

1.5913%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0248%

0.0117

64.2723%

1.1144%

GPU72

2⁶¹

0.1655

65.5738%

9000

150000

0.0013

1.6320%

0.1668

66.1356%

0.5618%

Difference

+15.8467

+3.0829%

+491000

+14850000

+0.1002

+3.4451%

+15.9469

+4.1124%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1855697	138232323858295871	18	56.940	37245391855 5 × 7 × 1489 × 714677	-	1489	714677	0.0058	0.0032	0.0057
1855697	48107172024300135660113	23	75.349	12962022362567848 2³ × 149 × 10874179834369	2021-06-08	149	10874179834369	5,594.4	46,604	87,043

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1855697

138232323858295871

56.940

37245391855
5 × 7 × 1489 × 714677

1489

714677

0.0058

0.0032

0.0057

1855697

48107172024300135660113

75.349

12962022362567848
2³ × 149 × 10874179834369

2021-06-08

149

10874179834369

5,594.4

46,604

87,043

exponent	prime factors	composite factor	digits	bits*
1855697	138232323858295871 48107172024300135660113	6649966183169807315456076534313847293423	40	132.289

exponent

prime factors

composite factor

digits

bits*

1855697

138232323858295871
48107172024300135660113

6649966183169807315456076534313847293423

132.289

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:36:22	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 138232323858295871	-	-	0.101	-	-	5.077%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:36:22

alpertron

Manual testing

500000

15000000

skipped known factor: 138232323858295871

0.101

-

-

5.077%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.565 GHz-days
Estimated T-Level:	24.554

Digits	B1	Curves	Complete	FacMiss
20	11000	255 / 100	2.550	7.709%
25	50000	255 / 280	0.911	40.158%

New Calculation Method

Total ECM effort:	19.565 GHz-days
Estimated T-Level:	24.554

Digits	B1	Complete	FacMiss
20	11000	8.711	0.016%
25	50000	0.789	45.424%
30	250000	0.049	95.236%
35	1000000	0.002	99.776%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.283
50000	5000000	48107172024300135660113	4	0.277
50000	6600000		218	17.01

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-17T21:01:18	Oliver Kruse	ECM-HTC	50000	5000000						3	0.208
2019-01-15T12:37:58	ATH	ec2-ECMCF	50000	5000000						3	0.208
2020-06-23T02:58:07	kracker	O0	50000	5000000						3	0.208
2020-07-20T04:59:57	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.208
2020-09-18T14:10:17	alpertron	colab	50000	5000000						7	0.484
2020-11-23T03:49:25	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2021-02-18T06:07:44	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.484
2021-06-08T03:40:43	Chang Chia-Tche	exbpc13	50000	5000000	48107172024300135660113	75.349	4	2	2556717137268035	4	0.277
2021-07-23T11:17:09	TJAOI	Manual testing	50000	6600000						218	17.01

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T07:32:56

Oliver Kruse

GTX-2

138232323858295871

AA0D30028684CF__

2017-11-07T04:27:42

kkmrkkblmbrbk

c4.xlarge

138232323858295871

AA0D30028684CF__

2021-06-08T13:32:02

mrh

lanai

138232323858295871

48107172024300135660113

15631DA9A0857F43

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)

10¹

10²

10³

10⁴

10⁵

10⁶

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