M1816489 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	16.3579	68.6567%	500000	15000000	0.1015	5.0641%	16.4594	70.2440%	1.5872%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8751%	0.0118	64.2171%	1.0592%
GPU72	2⁶¹	0.1691	65.5738%	9000	130000	0.0012	1.5573%	0.1703	66.1099%	0.5361%
Difference	+6	+16.1888	+3.0829%	+491000	+14870000	+0.1002	+3.5068%	+16.2890	+4.1341%	+4.1341%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3579

68.6567%

500000

15000000

0.1015

5.0641%

16.4594

70.2440%

1.5872%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8751%

0.0118

64.2171%

1.0592%

GPU72

2⁶¹

0.1691

65.5738%

9000

130000

0.0012

1.5573%

0.1703

66.1099%

0.5361%

Difference

+16.1888

+3.0829%

+491000

+14870000

+0.1002

+3.5068%

+16.2890

+4.1341%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1816489	43595737	8	25.378	12 2² × 3	-	4	4	2.467e-12	3.146e-7	6.404e-7
1816489	508616921	9	28.922	140 2² × 5 × 7	2008-07-15	5	7	2.028e-11	4.019e-7	8.005e-7
1816489	2164991359218315753582481	25	80.841	595927462048577160 2³ × 3 × 5 × 1180253 × 4207625131	2020-05-31	1180253	4207625131	225,837	18.121	33.680

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1816489

43595737

25.378

12
2² × 3

2.467e-12

3.146e-7

6.404e-7

1816489

508616921

28.922

140
2² × 5 × 7

2008-07-15

2.028e-11

4.019e-7

8.005e-7

1816489

2164991359218315753582481

80.841

595927462048577160
2³ × 3 × 5 × 1180253 × 4207625131

2020-05-31

1180253

4207625131

225,837

18.121

33.680

exponent	prime factors	composite factor	digits	bits*
1816489	43595737 508616921	22173529521665777	17	54.300
1816489	43595737 2164991359218315753582481	94384393903754219176138649483497	32	106.218
1816489	508616921 2164991359218315753582481	1101151239117224725392916205761001	34	109.763
1816489	43595737 508616921 2164991359218315753582481	48005499817778641298126796569394484452737	41	135.140

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:37:33	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 43595737 skipped known factor: 508616921	-	-	0.101	-	-	5.064%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	508616921	28.922	9	5.96564e-13	0.211	1.27734e-12

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.322 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:	17.322 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		212	14.63
50000	5000000	2164991359218315753582481	39	2.691

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-14T08:16:51	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-02T11:51:58	Ismo Laitela	6600K	50000	5000000						3	0.207
2019-10-04T00:13:54	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-01T18:31:08	Greg	azure2	50000	5000000						3	0.207
2020-06-01T02:18:17	nordi	sweet16	50000	5000000	2164991359218315753582481	80.841	39	2	2270902000241974	39	2.691
2021-02-26T17:52:56	TJAOI	Manual testing	50000	5000000						202	13.94

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T22:13:47

Oliver Kruse

GTX-3

43595737

508616921

DBA6A2D156C00A__

2017-11-05T21:44:18

kkmrkkblmbrbk

c4.xlarge

43595737

508616921

DBA6A2D156C00A__

2020-06-01T04:19:57

CrypticClue

cruncher

43595737

508616921

2164991359218315753582481

C54BDCADD1095519

2020-06-02T13:46:52

Luigi Morelli

9800X

43595737

508616921

2164991359218315753582481

C54BDCADD1095519

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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