M2018437 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	14.7213	68.6567%	500000	15000000	0.1230	5.1287%	14.8442	70.2642%	1.6075%
PrimeNet	2⁵⁸	0.0190	63.7931%	9000	150000	0.0016	2.6116%	0.0206	64.7387%	0.9456%
GPU72	2⁶²	0.3044	66.1290%	8000	120000	0.0013	1.2731%	0.3057	66.5602%	0.4312%
Difference	+5	+14.4169	+2.5277%	+492000	+14880000	+0.1216	+3.8556%	+14.5385	+3.7040%	+3.7040%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.7213

68.6567%

500000

15000000

0.1230

5.1287%

14.8442

70.2642%

1.6075%

PrimeNet

2⁵⁸

0.0190

63.7931%

9000

150000

0.0016

2.6116%

0.0206

64.7387%

0.9456%

GPU72

2⁶²

0.3044

66.1290%

8000

120000

0.0013

1.2731%

0.3057

66.5602%

0.4312%

Difference

+14.4169

+2.5277%

+492000

+14880000

+0.1216

+3.8556%

+14.5385

+3.7040%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2018437	60553111	8	25.852	15 3 × 5	-	3	5	2.222e-12	2.964e-7	5.821e-7
2018437	1852925167	10	30.787	459 3³ × 17	2008-07-15	27	27	7.791e-11	2.574e-6	5.239e-6
2018437	534060671732801031529	21	68.856	132295600935972 2² × 3² × 115117 × 31922981	2019-05-24	115117	31922981	29.607	0.1762	0.3097

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2018437

60553111

25.852

15
3 × 5

2.222e-12

2.964e-7

5.821e-7

2018437

1852925167

30.787

459
3³ × 17

2008-07-15

7.791e-11

2.574e-6

5.239e-6

2018437

534060671732801031529

68.856

132295600935972
2² × 3² × 115117 × 31922981

2019-05-24

115117

31922981

29.607

0.1762

0.3097

exponent	prime factors	composite factor	digits	bits*
2018437	60553111 1852925167	112200383312044537	18	56.639
2018437	60553111 534060671732801031529	32339035136170863203090036719	29	94.707
2018437	1852925167 534060671732801031529	989574459358632530723644590343	30	99.643
2018437	60553111 1852925167 534060671732801031529	59921812080308264441119761203589207073	38	125.494

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:19:37	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 60553111 skipped known factor: 1852925167	-	-	0.123	-	-	5.129%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:49:00	J Feitsma	Manual testing	?	?	1852925167	30.787	10	7.04075e-12	0.289	1.53104e-11

ECM factoring results:

Old Calculation Method

Total ECM effort:

31.330 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	369 / 100	3.690	2.451%
25	50000	369 / 280	1.318	26.708%

New Calculation Method

Total ECM effort:

31.330 GHz-days

Digits	B1	Complete	FacMiss
20	11000	11.919	0.001%
25	50000	1.078	34.043%
30	250000	0.066	93.579%
35	1000000	0.003	99.697%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		360	30.48
50000	5000000	534060671732801031529	2	0.169
50000	6750000		7	0.677

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-27T10:20:17	Oliver Kruse	ECM-HTC	50000	5000000						3	0.254
2019-05-24T20:10:08	MarkS	laptop64	50000	5000000	534060671732801031529	68.856	2	2		2	0.169
2021-04-25T16:59:21	nordi	sweet16	50000	6750000						7	0.677
2021-08-10T20:48:47	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.593
2021-12-29T14:05:25	Barney_Jr	Manual testing	50000	5000000						350	29.64

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T23:18:22

Oliver Kruse

GTX-1

60553111

1852925167

BB1E01A40121FE__

2017-11-13T22:56:26

kkmrkkblmbrbk

c4.xlarge

60553111

1852925167

BB1E01A40121FE__

2019-05-28T23:09:28

vnatin

VIR10-1255

60553111

1852925167

534060671732801031529

26346E494045A81F

2019-05-29T21:57:45

kkmrkkblmbrbk

c5.large

60553111

1852925167

534060671732801031529

26346E494045A81F

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