M1836059 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	16.1835	68.6567%	500000	15000000	0.1015	5.0706%	16.2850	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	+16.0162	+3.0829%	+491000	+14860000	+0.1002	+3.4749%	+16.1164	+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

16.1835

68.6567%

500000

15000000

0.1015

5.0706%

16.2850

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

+16.0162

+3.0829%

+491000

+14860000

+0.1002

+3.4749%

+16.1164

+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
1836059	58753889	8	25.808	16 2⁴	-	16	16	2.443e-12	1.259e-6	2.561e-6
1836059	47727418861740368922553	23	75.337	12997245421236564 2² × 3² × 59 × 6119230424311	2019-01-04	59	6119230424311	5,163.5	26,225	48,982
1836059	98503337005065459273647	23	76.383	26824665494154997 7 × 14241103 × 269086957	2020-10-13	14241103	269086957	12,516	2.2124	2.2799

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1836059

58753889

25.808

16
2⁴

2.443e-12

1.259e-6

2.561e-6

1836059

47727418861740368922553

75.337

12997245421236564
2² × 3² × 59 × 6119230424311

2019-01-04

6119230424311

5,163.5

26,225

48,982

1836059

98503337005065459273647

76.383

26824665494154997
7 × 14241103 × 269086957

2020-10-13

14241103

269086957

12,516

2.2124

2.2799

exponent	prime factors	composite factor	digits	bits*
1836059	58753889 47727418861740368922553	2804171470059199982494728558617	31	101.145
1836059	58753889 98503337005065459273647	5787454128525208431897876463183	31	102.191
1836059	47727418861740368922553 98503337005065459273647	4701310024519929262963002556041733131376860791	46	151.720
1836059	58753889 47727418861740368922553 98503337005065459273647	27622024733523120220398006328439226776853849608286 6199	54	177.528

	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: 58753889	-	-	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: 58753889

0.101

-

-

5.071%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.822 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.822 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.825	0.015%
25	50000	0.800	44.941%
30	250000	0.049	95.172%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.004
50000	5000000	47727418861740368922553	2	0.138
50000	5000000	98503337005065459273647	1	0.069
50000	6600000		219	17.06
50000	6750000		7	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-15T06:11:39	ATH	ec2-1xe	50000	5000000						3	0.207
2019-01-04T08:23:17	Chang Chia-Tche	exbpc13	50000	5000000	47727418861740368922553	75.337	2	2		2	0.138
2020-05-06T09:51:10	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-12T19:52:19	nordi	sweet16	50000	5000000						3	0.207
2020-07-07T00:47:12	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-08-09T07:57:06	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-10-13T21:47:05	nordi	sweet16	50000	5000000	98503337005065459273647	76.383	1	2	8980999696263336	1	0.069
2020-10-22T07:00:03	nordi	sweet16	50000	5000000						7	0.484
2021-01-15T09:26:08	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-04-09T18:20:37	Bommer	3900X	50000	6750000						7	0.551
2021-05-14T12:08:42	TJAOI	Manual testing	50000	6600000						219	17.06

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T02:59:31

Oliver Kruse

GTX-0

58753889

43CFF17626423B__

2017-11-06T10:59:14

kkmrkkblmbrbk

c4.xlarge

58753889

43CFF17626423B__

2019-01-05T20:14:00

GunnarLu

Ribenboim

58753889

47727418861740368922553

9C5D245E7A3F0CDC

2019-01-06T16:53:27

kkmrkkblmbrbk

c5.large

58753889

47727418861740368922553

9C5D245E7A3F0CDC

2020-10-14T14:15:26

mrh.org

lanai

58753889

47727418861740368922553

98503337005065459273647

9C5D245E7A3F0CDC

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

10⁷

10⁸

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