M1334651 Mersenne number exponent details

Residue

Status

L-L

1220684BBD5B6C82

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	22.2634	68.6567%	500000	15000000	0.0714	4.8789%	22.3349	70.1859%	1.5292%
PrimeNet	2⁵⁶	0.0072	62.5000%	6000	100000	0.0006	2.6071%	0.0078	63.4777%	0.9777%
GPU72	2⁶⁰	0.1151	65.0000%	5500	40000	0.0004	0.9791%	0.1155	65.3427%	0.3427%
Difference	+7	+22.1484	+3.6567%	+494500	+14960000	+0.0710	+3.8998%	+22.2194	+4.8432%	+4.8432%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

22.2634

68.6567%

500000

15000000

0.0714

4.8789%

22.3349

70.1859%

1.5292%

PrimeNet

2⁵⁶

0.0072

62.5000%

6000

100000

0.0006

2.6071%

0.0078

63.4777%

0.9777%

GPU72

2⁶⁰

0.1151

65.0000%

5500

40000

0.0004

0.9791%

0.1155

65.3427%

0.3427%

Difference

+22.1484

+3.6567%

+494500

+14960000

+0.0710

+3.8998%

+22.2194

+4.8432%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1334651	54191169989810818033	20	65.555	20301625664616 2³ × 3 × 41 × 20631733399	2009-04-12	41	20631733399	7.6914	62.231	116.23
1334651	12469944725980298843599	23	73.401	4671612551138949 3² × 13 × 39928312402897	2018-08-24	13	39928312402897	2,255.1	120,434	224,938

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1334651

54191169989810818033

65.555

20301625664616
2³ × 3 × 41 × 20631733399

2009-04-12

20631733399

7.6914

62.231

116.23

1334651

12469944725980298843599

73.401

4671612551138949
3² × 13 × 39928312402897

2018-08-24

39928312402897

2,255.1

120,434

224,938

exponent	prime factors	composite factor	digits	bits*
1334651	54191169989810818033 12469944725980298843599	675760894409143255352831603455530115820767	42	138.956

exponent

prime factors

composite factor

digits

bits*

1334651

54191169989810818033
12469944725980298843599

675760894409143255352831603455530115820767

138.956

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	Team Prime Rib	v4_computers	15000	213750		-		-	-	0.001	-	-	0.791%
2016-03-17T19:05:09	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.879%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.029	-	-
2022-03-07T17:32:34	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.086	-	-
2009-02-24T04:24:00	Sturle Sunde	jodel.ifi	2⁶⁰	2⁶¹		-	-	0.115	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.106 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	300 / 100	3.000	4.904%
25	50000	300 / 280	1.071	34.186%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.106 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.615	0.000%
25	50000	1.647	19.258%
30	250000	0.141	86.886%
35	1000000	0.010	99.022%

ECM Summary

B1	B2	factor	curves	GHz-days
		54191169989810818033	1	0.00000e+0
50000	5000000		92	4.294
50000	5000000	12469944725980298843599	158	7.375
250000	35000000		50	13.44

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-20T10:28:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-10-20T11:17:00	arnaud	TECH03	50000	5000000						3	0.140
2009-04-12T16:15:00	SubPrime	c2d0			54191169989810818033	65.555		1		1	-
2018-08-24T12:41:10	TJAOI	Manual testing	50000	5000000	12469944725980298843599	73.401	158	2		158	7.375
2018-08-24T12:41:10	TJAOI	Manual testing	50000	5000000						88	4.107
2021-07-16T08:44:55	TJAOI	Manual testing	250000	35000000						50	13.44

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T05:09:19

Oliver Kruse

GTX-0

54191169989810818033

8F4D638B87AD63__

2017-10-24T00:31:35

kkmrkkblmbrbk

c4.xlarge

54191169989810818033

8F4D638B87AD63__

2018-08-27T11:45:12

ANONYMOUS

dory

54191169989810818033

12469944725980298843599

6DE7C4027E7236__

2018-08-28T13:32:38

Oliver Kruse

GTX-4

54191169989810818033

12469944725980298843599

6DE7C4027E7236__

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 = 15000, B2 = 213750 (P-1 stage 2)

B1 = 15000 (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