M1836047 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	16.1836	68.6567%	500000	15000000	0.1015	5.0706%	16.2851	70.2460%	1.5893%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8809%	0.0117	64.2193%	1.0614%
GPU72	2⁶¹	0.1673	65.5738%	9000	140000	0.0013	1.5957%	0.1686	66.1231%	0.5493%
Difference	+6	+16.0163	+3.0829%	+491000	+14860000	+0.1002	+3.4749%	+16.1165	+4.1229%	+4.1229%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1836

68.6567%

500000

15000000

0.1015

5.0706%

16.2851

70.2460%

1.5893%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8809%

0.0117

64.2193%

1.0614%

GPU72

2⁶¹

0.1673

65.5738%

9000

140000

0.0013

1.5957%

0.1686

66.1231%

0.5493%

Difference

+16.0163

+3.0829%

+491000

+14860000

+0.1002

+3.4749%

+16.1165

+4.1229%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1836047	47737223	8	25.509	13 13	-	1	13	2.441e-12	1.301e-7	1.601e-7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1836047

47737223

25.509

13
13

2.441e-12

1.301e-7

1.601e-7

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:40:11	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 47737223	-	-	0.101	-	-	5.071%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:40:11

alpertron

Manual testing

500000

15000000

skipped known factor: 47737223

0.101

-

-

5.071%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.235 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:	19.235 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	10.343	0.003%
25	50000	0.952	38.602%
30	250000	0.060	94.138%
35	1000000	0.003	99.717%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	2.487
50000	6600000		215	16.75

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-15T19:34:33	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-01-04T07:43:36	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-16T02:13:50	nordi	sweet16	50000	5000000						3	0.207
2020-06-21T20:13:20	MarkS	laptop64	50000	5000000						3	0.207
2020-07-19T00:51:37	argusdusty	Argus-PC	50000	5000000						3	0.207
2020-09-13T03:17:22	Jack Rhys-Burgess	Temp	50000	5000000						7	0.484
2020-11-22T00:19:32	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2021-02-16T21:23:07	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.484
2021-04-30T08:11:27	TJAOI	Manual testing	50000	6600000						215	16.75

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

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