M1836433 Mersenne number exponent details

Residue

Status

L-L

FE30440F7FB98E75

double-checked

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	16.1802	68.6567%	500000	15000000	0.1015	5.0707%	16.2817	70.2460%	1.5893%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8810%	0.0117	64.2193%	1.0614%
GPU72	2⁶¹	0.1673	65.5738%	9000	140000	0.0013	1.5957%	0.1685	66.1231%	0.5494%
Difference	+6	+16.0130	+3.0829%	+491000	+14860000	+0.1002	+3.4750%	+16.1132	+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

16.1802

68.6567%

500000

15000000

0.1015

5.0707%

16.2817

70.2460%

1.5893%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8810%

0.0117

64.2193%

1.0614%

GPU72

2⁶¹

0.1673

65.5738%

9000

140000

0.0013

1.5957%

0.1685

66.1231%

0.5494%

Difference

+16.0130

+3.0829%

+491000

+14860000

+0.1002

+3.4750%

+16.1132

+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
1836433	1833759135139922743	19	60.670	499271994987 3 × 857 × 4561 × 42577	2009-07-21	4561	42577	0.1156	0.0005	0.0007
1836433	2562668362999409142202937	25	81.084	697729882603778396 2² × 191 × 2657 × 2707 × 126973811	2021-01-20	2707	126973811	519,269	0.5444	1.0164

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1836433

1833759135139922743

60.670

499271994987
3 × 857 × 4561 × 42577

2009-07-21

4561

42577

0.1156

0.0005

0.0007

1836433

2562668362999409142202937

81.084

697729882603778396
2² × 191 × 2657 × 2707 × 126973811

2021-01-20

2707

126973811

519,269

0.5444

1.0164

exponent	prime factors	composite factor	digits	bits*
1836433	1833759135139922743 2562668362999409142202937	4699316520984238100867346782135807007696191	43	141.753

exponent

prime factors

composite factor

digits

bits*

1836433

1833759135139922743
2562668362999409142202937

4699316520984238100867346782135807007696191

141.753

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:40:13	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1833759135139922743	-	-	0.101	-	-	5.071%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:40:13

alpertron

Manual testing

500000

15000000

skipped known factor: 1833759135139922743

0.101

-

-

5.071%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-01-16T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.021

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.146 GHz-days
Estimated T-Level:	24.446

Digits	B1	Curves	Complete	FacMiss
20	11000	249 / 100	2.490	8.188%
25	50000	249 / 280	0.889	41.030%

New Calculation Method

Total ECM effort:	19.146 GHz-days
Estimated T-Level:	24.446

Digits	B1	Complete	FacMiss
20	11000	8.522	0.020%
25	50000	0.772	46.197%
30	250000	0.048	95.334%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
		1833759135139922743	1	0.00000e+0
50000	5000000		29	2.004
50000	6600000		215	16.75
50000	6750000	2562668362999409142202937	5	0.394

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-10T18:35:00	Scott Kurowski	UW4	50000	5000000						3	0.207
2009-07-21T04:52:00	Piepen	T41-2000			1833759135139922743	60.670		1		1	-
2020-05-06T16:48:09	Greg Hogan	azure3	50000	5000000						3	0.207
2020-06-13T15:40:53	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-07-08T10:09:17	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-08-09T23:58:22	Ahmed Azhad	c5.xlarge.az	50000	5000000						3	0.207
2020-10-14T12:45:15	nordi	sweet16	50000	5000000						7	0.484
2021-01-20T21:33:20	nordi	sweet16	50000	6750000	2562668362999409142202937	81.084	5	2	8754427454203234	5	0.394
2021-02-22T01:25:49	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.484
2021-05-28T18:41:07	TJAOI	Manual testing	50000	6600000						215	16.75

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	FE30440F7FB98E75	0.100

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

FE30440F7FB98E75

0.100

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T03:16:02

Oliver Kruse

GTX-0

1833759135139922743

B1B4674D92B4AB__

2017-11-06T11:09:23

ATH

ec2-1xf

1833759135139922743

B1B4674D92B4AB__

2021-01-23T09:40:58

Sébastien Broucke

Portable_Seb

1833759135139922743

2562668362999409142202937

4C1CE0949770A556

2021-01-23T10:02:10

rucio

1833759135139922743

2562668362999409142202937

4C1CE0949770A556

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)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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