M1566211 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	18.9718	68.6567%	500000	15000000	0.0835	4.9743%	19.0554	70.2158%	1.5591%
PrimeNet	2⁵⁷	0.0123	63.1579%	7000	110000	0.0008	2.4763%	0.0131	64.0702%	0.9123%
GPU72	2⁶¹	0.1961	65.5738%	6500	60000	0.0006	1.0513%	0.1967	65.9357%	0.3619%
Difference	+6	+18.7757	+3.0829%	+493500	+14940000	+0.0829	+3.9229%	+18.8587	+4.2801%	+4.2801%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.9718

68.6567%

500000

15000000

0.0835

4.9743%

19.0554

70.2158%

1.5591%

PrimeNet

2⁵⁷

0.0123

63.1579%

7000

110000

0.0008

2.4763%

0.0131

64.0702%

0.9123%

GPU72

2⁶¹

0.1961

65.5738%

6500

60000

0.0006

1.0513%

0.1967

65.9357%

0.3619%

Difference

+18.7757

+3.0829%

+493500

+14940000

+0.0829

+3.9229%

+18.8587

+4.2801%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1566211	66950110569735689	17	55.894	21373273004 2² × 137 × 2591 × 15053	-	2591	15053	0.0048	0.0002	0.0003
1566211	1205820229623666130273	22	70.031	384948206092176 2⁴ × 3 × 29 × 276543251503	2017-12-04	29	276543251503	270.74	975.83	1,822.6
1566211	8521571729396542054729	22	72.852	2720441795325324 2² × 3 × 7 × 32386211849111	2022-05-12	7	32386211849111	843.79	114,280	213,443

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1566211

66950110569735689

55.894

21373273004
2² × 137 × 2591 × 15053

2591

15053

0.0048

0.0002

0.0003

1566211

1205820229623666130273

70.031

384948206092176
2⁴ × 3 × 29 × 276543251503

2017-12-04

276543251503

270.74

975.83

1,822.6

1566211

8521571729396542054729

72.852

2720441795325324
2² × 3 × 7 × 32386211849111

2022-05-12

32386211849111

843.79

114,280

213,443

exponent	prime factors	composite factor	digits	bits*
1566211	66950110569735689 1205820229623666130273	80729797700528525359829313467051413097	38	125.924
1566211	66950110569735689 8521571729396542054729	570520169511032264794393011958502523281	39	128.746
1566211	1205820229623666130273 8521571729396542054729	10275483579495480036557991013721339609711017	44	142.882
1566211	66950110569735689 1205820229623666130273 8521571729396542054729	68794476180472584992240511076176739487584553290356 7361385713	60	198.776

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:16:24	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 66950110569735689	-	-	0.084	-	-	4.974%

ECM factoring results:

Old Calculation Method

Total ECM effort:	31.285 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	31.285 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.390	24.916%
30	250000	0.116	89.004%
35	1000000	0.008	99.198%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	13.88
50000	5000000	1205820229623666130273	3	0.168
250000	40000000		6	2.069
250000	40000000	8521571729396542054729	44	15.17

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-04T06:32:10	Chang Chia-Tche	exbpc13	50000	5000000	1205820229623666130273	70.031	3	2		3	0.168
2018-11-13T09:11:54	rucio		50000	5000000						3	0.168
2019-08-19T13:18:05	TJAOI	Manual testing	50000	5000000						245	13.71
2022-05-12T09:16:57	TJAOI	Manual testing	250000	40000000	8521571729396542054729	72.852	44	2		44	15.17
2022-05-12T09:16:57	TJAOI	Manual testing	250000	40000000						6	2.069

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T21:26:59

Oliver Kruse

GTX-1

66950110569735689

FD72CE91E874C4__

2017-10-31T04:23:19

Chang Chia-Tche

homura

66950110569735689

FD72CE91E874C4__

2017-12-04T22:17:28

kkmrkkblmbrbk

c4.xlarge

66950110569735689

1205820229623666130273

0E1C97B25EA8A4__

2017-12-05T14:49:47

Oliver Kruse

Threadripper

66950110569735689

1205820229623666130273

0E1C97B25EA8A4__

2022-05-12T17:01:16

aperson1

2012_VP113

66950110569735689

1205820229623666130273

8521571729396542054729

0E1C97B25EA8A4DE

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

10¹¹

10¹²

10¹³

10¹⁴

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