M1666039 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	17.8351	68.6567%	500000	15000000	0.0880	5.0115%	17.9231	70.2275%	1.5708%
PrimeNet	2⁵⁷	0.0115	63.1579%	7000	120000	0.0009	2.5683%	0.0124	64.1041%	0.9462%
GPU72	2⁶¹	0.1844	65.5738%	7000	80000	0.0007	1.2061%	0.1851	65.9890%	0.4152%
Difference	+6	+17.6507	+3.0829%	+493000	+14920000	+0.0873	+3.8054%	+17.7380	+4.2385%	+4.2385%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.8351

68.6567%

500000

15000000

0.0880

5.0115%

17.9231

70.2275%

1.5708%

PrimeNet

2⁵⁷

0.0115

63.1579%

7000

120000

0.0009

2.5683%

0.0124

64.1041%

0.9462%

GPU72

2⁶¹

0.1844

65.5738%

7000

80000

0.0007

1.2061%

0.1851

65.9890%

0.4152%

Difference

+17.6507

+3.0829%

+493000

+14920000

+0.0873

+3.8054%

+17.7380

+4.2385%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1666039	75788114111	11	36.141	22745 5 × 4549	-	5	4549	1.057e-8	1.724e-5	3.156e-5
1666039	179287092510769837417	21	67.281	53806391240172 2² × 3 × 2371 × 1891128611	2019-03-08	2371	1891128611	23.940	7.0313	13.132

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1666039

75788114111

36.141

22745
5 × 4549

4549

1.057e-8

1.724e-5

3.156e-5

1666039

179287092510769837417

67.281

53806391240172
2² × 3 × 2371 × 1891128611

2019-03-08

2371

1891128611

23.940

7.0313

13.132

exponent	prime factors	composite factor	digits	bits*
1666039	75788114111 179287092510769837417	13587830625835637934616513491287	32	103.422

exponent

prime factors

composite factor

digits

bits*

1666039

75788114111
179287092510769837417

13587830625835637934616513491287

103.422

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:07	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 75788114111	-	-	0.088	-	-	5.012%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.888 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:	14.888 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		248	14.71
50000	5000000	179287092510769837417	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-07-02T07:40:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-01-24T13:44:33	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-03-08T09:17:57	Chang Chia-Tche	exbpc13	50000	5000000	179287092510769837417	67.281	3	2		3	0.178
2019-12-02T14:37:12	TJAOI	Manual testing	50000	5000000						244	14.47

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T01:21:05

Oliver Kruse

Doppelherz

75788114111

67549B3C482AE5__

2017-11-02T21:05:12

kkmrkkblmbrbk

c4.xlarge

75788114111

67549B3C482AE5__

2019-03-09T06:57:25

artorollo

fourth

75788114111

179287092510769837417

534724C819B42374

2019-03-09T20:19:44

kkmrkkblmbrbk

c5.large

75788114111

179287092510769837417

534724C819B42374

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

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