M16783453 Mersenne number exponent details

Residue

Status

L-L

C0793D43E9E32F22

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	1.7704	62.6866%	210000	5302500	0.3865	4.9137%	2.1569	64.5200%	1.8335%
PrimeNet	2⁶⁵	0.4347	61.5385%	80000	2400000	0.1636	4.5220%	0.5983	63.2777%	1.7392%
GPU72	2⁶⁹	7.1134	63.7681%	120000	3200000	0.2282	3.2893%	7.3416	64.9599%	1.1918%
Difference	-2	-5.3429	-1.0815%	+90000	+2102500	+0.1583	+1.6244%	-5.1846	-0.4399%	-0.4399%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.7704

62.6866%

210000

5302500

0.3865

4.9137%

2.1569

64.5200%

1.8335%

PrimeNet

2⁶⁵

0.4347

61.5385%

80000

2400000

0.1636

4.5220%

0.5983

63.2777%

1.7392%

GPU72

2⁶⁹

7.1134

63.7681%

120000

3200000

0.2282

3.2893%

7.3416

64.9599%

1.1918%

Difference

-2

-5.3429

-1.0815%

+90000

+2102500

+0.1583

+1.6244%

-5.1846

-0.4399%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16783453	665729831798293397657	21	69.173	19832922098876 2² × 19 × 149 × 1751406049	2017-06-08	149	1751406049	8.1249	75.657	141.31

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16783453

665729831798293397657

69.173

19832922098876
2² × 19 × 149 × 1751406049

2017-06-08

149

1751406049

8.1249

75.657

141.31

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-10-26T00:00:00	ANONYMOUS	v4_computers	210000	5302500		-		-	-	0.386	-	-	4.914%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2001-07-17T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁶¹		-	-	0.018	-	-
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.212	-	-
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.435	-	-
2016-03-16T13:00:04	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.445	-	-
2014-09-16T13:08:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.890	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	665729831798293397657	1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-08T07:49:16	ATH	ec2-1x	50000	5000000	665729831798293397657	69.173	1	2		1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-11-02T00:00:00	ANONYMOUS	v4_computers	C0793D43E9E32F22	9.177
2006-12-18T00:00:00	TwistedFate2k	v4_computers	C0793D43E9E32F22	9.177

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 = 210000, B2 = 5302500 (P-1 stage 2)

B1 = 210000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶¹

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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