M1709767 Mersenne number exponent details

Residue

Status

L-L

F0A2F5D8404FC537

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	17.3789	68.6567%	3000000	273000000	1.2086	9.5092%	18.5875	71.6372%	2.9805%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7902%	0.0123	64.1858%	1.0280%
GPU72	2⁶¹	0.1797	65.5738%	7000	100000	0.0008	1.3029%	0.1805	66.0223%	0.4485%
Difference	+6	+17.1993	+3.0829%	+2993000	+272900000	+1.2077	+8.2062%	+18.4070	+5.6149%	+5.6149%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.3789

68.6567%

3000000

273000000

1.2086

9.5092%

18.5875

71.6372%

2.9805%

PrimeNet

2⁵⁷

0.0112

63.1579%

8000

140000

0.0010

2.7902%

0.0123

64.1858%

1.0280%

GPU72

2⁶¹

0.1797

65.5738%

7000

100000

0.0008

1.3029%

0.1805

66.0223%

0.4485%

Difference

+17.1993

+3.0829%

+2993000

+272900000

+1.2077

+8.2062%

+18.4070

+5.6149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1709767	21252139091863656593	20	64.204	6214922586488 2³ × 7 × 11 × 709 × 14230127	2010-07-12	709	14230127	2.2274	0.0530	0.0988
1709767	23345416044462901044363817	26	84.271	6827075281153192524 2² × 3 × 42703 × 47407 × 281029937	2020-03-29	47407	281029937	4,237,718	1.0479	1.9515

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1709767

21252139091863656593

64.204

6214922586488
2³ × 7 × 11 × 709 × 14230127

2010-07-12

709

14230127

2.2274

0.0530

0.0988

1709767

23345416044462901044363817

84.271

6827075281153192524
2² × 3 × 42703 × 47407 × 281029937

2020-03-29

47407

281029937

4,237,718

1.0479

1.9515

exponent	prime factors	composite factor	digits	bits*
1709767	21252139091863656593 23345416044462901044363817	496140028934351035867317366122541743042695481	45	148.476

exponent

prime factors

composite factor

digits

bits*

1709767

21252139091863656593
23345416044462901044363817

496140028934351035867317366122541743042695481

148.476

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:30:07	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 21252139091863656593	-	-	0.088	-	-	5.027%
2021-07-17T23:10:44	Dylan Delgado	laptop-ryzen73700	3000000	273000000		-	skipped known factor: 21252139091863656593	-	-	1.209	-	-	9.509%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2022-03-08T23:06:23	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2022-03-09T02:40:39	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.090	-	-
2010-04-24T12:42:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.090	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.999 GHz-days
Estimated T-Level:	24.804

Digits	B1	Curves	Complete	FacMiss
20	11000	269 / 100	2.690	6.697%
25	50000	269 / 280	0.961	38.196%

New Calculation Method

Total ECM effort:	15.999 GHz-days
Estimated T-Level:	24.804

Digits	B1	Complete	FacMiss
20	11000	8.677	0.017%
25	50000	0.784	45.646%
30	250000	0.048	95.285%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
		21252139091863656593	1	0.00000e+0
50000	5000000		268	15.94
50000	5000000	23345416044462901044363817	1	0.059

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-27T18:26:00	Team_Bundu	bundu4	50000	5000000						3	0.178
2009-06-21T08:51:00	James Hintz	05_060309	50000	5000000						3	0.178
2010-07-12T18:14:00	Lupo	yorick			21252139091863656593	64.204		1		1	-
2020-02-05T06:18:36	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-12T22:38:46	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-21T01:25:35	kracker	O0	50000	5000000						3	0.178
2020-02-28T21:49:33	kracker	O0	50000	5000000						3	0.178
2020-03-11T09:24:54	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-29T08:25:01	MarkS	desktop-i7	50000	5000000	23345416044462901044363817	84.271	1	2	4259639428268665	1	0.059
2020-04-12T16:16:44	Oliver Kruse	IOS-2	50000	5000000						3	0.178
2020-04-20T10:34:19	TJAOI	Manual testing	50000	5000000						190	11.30
2020-04-20T10:35:00	TJAOI	Manual testing	50000	5000000						54	3.212

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	F0A2F5D8404FC537	0.080

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

ANONYMOUS

v4_computers

F0A2F5D8404FC537

0.080

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:15:19

alpertron

Manual testing

21252139091863656593

F5F7DAFEE57990__

2017-10-18T21:46:52

Oliver Kruse

Threadripper

21252139091863656593

F5F7DAFEE57990__

2020-03-30T20:54:43

AbsolutXTR

750D

21252139091863656593

23345416044462901044363817

38DAB6FF1D429049

2020-04-02T14:50:25

oodaira

com1

21252139091863656593

23345416044462901044363817

38DAB6FF1D429049

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 = 3000000, B2 = 273000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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