M1584827 Mersenne number exponent details

Residue

Status

L-L

210E77E8096C7950

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	18.7490	68.6567%	500000	15000000	0.0835	4.9814%	18.8325	70.2180%	1.5613%
PrimeNet	2⁵⁷	0.0121	63.1579%	7000	120000	0.0009	2.5434%	0.0130	64.0949%	0.9370%
GPU72	2⁶¹	0.1938	65.5738%	6500	60000	0.0006	1.0541%	0.1944	65.9367%	0.3629%
Difference	+6	+18.5552	+3.0829%	+493500	+14940000	+0.0829	+3.9273%	+18.6381	+4.2814%	+4.2814%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.7490

68.6567%

500000

15000000

0.0835

4.9814%

18.8325

70.2180%

1.5613%

PrimeNet

2⁵⁷

0.0121

63.1579%

7000

120000

0.0009

2.5434%

0.0130

64.0949%

0.9370%

GPU72

2⁶¹

0.1938

65.5738%

6500

60000

0.0006

1.0541%

0.1944

65.9367%

0.3629%

Difference

+18.5552

+3.0829%

+493500

+14940000

+0.0829

+3.9273%

+18.6381

+4.2814%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1584827	119095709254038532817	21	66.691	37573725477304 2³ × 107 × 19661 × 2232569	2013-04-09	19661	2232569	13.123	0.0091	0.0147

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1584827

119095709254038532817

66.691

37573725477304
2³ × 107 × 19661 × 2232569

2013-04-09

19661

2232569

13.123

0.0091

0.0147

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-02T17:11:00	James Heinrich	WHS	85000	1402500		-		-	-	0.010	-	-	2.259%
2016-03-17T19:17:02	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 119095709254038532817	-	-	0.084	-	-	4.981%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2022-03-09T01:21:19	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.097	-	-
2010-05-06T12:30:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.097	-	-
2010-06-23T00:16:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.007	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.947 GHz-days
Estimated T-Level:	24.446

Digits	B1	Curves	Complete	FacMiss
20	11000	249 / 100	2.490	8.188%
25	50000	249 / 280	0.889	41.030%

New Calculation Method

Total ECM effort:	13.947 GHz-days
Estimated T-Level:	24.446

Digits	B1	Complete	FacMiss
20	11000	8.032	0.032%
25	50000	0.726	48.387%
30	250000	0.045	95.628%
35	1000000	0.002	99.796%

ECM Summary

B1	B2	factor	curves	GHz-days
		119095709254038532817	1	0.00000e+0
50000	5000000		249	13.95

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-15T16:54:00	Rob_Dee	twopc	50000	5000000						1	0.056
2009-04-16T06:07:00	Adel El-Atawy	SRVRARC	50000	5000000						3	0.168
2009-07-23T12:35:00	James Hintz	05_071509	50000	5000000						3	0.168
2010-09-12T04:15:00	Martti Järvi	Tiny	50000	5000000						3	0.168
2011-12-03T07:52:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.168
2013-04-09T18:44:00	Chang Chia-Tche	exbpc13			119095709254038532817	66.691		1		1	-
2019-09-02T12:31:07	TJAOI	Manual testing	50000	5000000						236	13.22

date	userid	compid	res64	spent (GHz-days)
1998-11-14T00:00:00	ANONYMOUS	v4_computers	210E77E8096C7950	0.071

date

userid

compid

res64

spent (GHz-days)

1998-11-14T00:00:00

ANONYMOUS

v4_computers

210E77E8096C7950

0.071

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T00:43:28

Oliver Kruse

GTX-2

119095709254038532817

AF09744B0C1A52__

2017-10-31T16:29:40

kkmrkkblmbrbk

old

119095709254038532817

AF09744B0C1A52__

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)

B1 = 85000, B2 = 1402500 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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