M1468963 Mersenne number exponent details

Residue

Status

L-L

09E6AB18497B595E

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	20.2278	68.6567%	500000	15000000	0.0714	4.9359%	20.2992	70.2038%	1.5471%
PrimeNet	2⁵⁶	0.0065	62.5000%	7000	120000	0.0007	2.9114%	0.0073	63.5918%	1.0918%
GPU72	2⁶⁰	0.1046	65.0000%	6500	100000	0.0006	1.4469%	0.1052	65.5064%	0.5064%
Difference	+7	+20.1233	+3.6567%	+493500	+14900000	+0.0708	+3.4890%	+20.1940	+4.6974%	+4.6974%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.2278

68.6567%

500000

15000000

0.0714

4.9359%

20.2992

70.2038%

1.5471%

PrimeNet

2⁵⁶

0.0065

62.5000%

7000

120000

0.0007

2.9114%

0.0073

63.5918%

1.0918%

GPU72

2⁶⁰

0.1046

65.0000%

6500

100000

0.0006

1.4469%

0.1052

65.5064%

0.5064%

Difference

+20.1233

+3.6567%

+493500

+14900000

+0.0708

+3.4890%

+20.1940

+4.6974%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1468963	794664191843452484127491471	27	89.360	270484754157678744845 5 × 7 × 23 × 83 × 433 × 2203 × 4621 × 918397	2009-06-06	4621	918397	105,390,768	0.0030	0.0052
1468963	3085683995023346665933859543	28	91.318	1050293300451865249817 43 × 103 × 107 × 267389 × 8288531651	2019-04-26	267389	8288531651	457,918,732	25.014	46.694

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1468963

794664191843452484127491471

89.360

270484754157678744845
5 × 7 × 23 × 83 × 433 × 2203 × 4621 × 918397

2009-06-06

4621

918397

105,390,768

0.0030

0.0052

1468963

3085683995023346665933859543

91.318

1050293300451865249817
43 × 103 × 107 × 267389 × 8288531651

2019-04-26

267389

8288531651

457,918,732

25.014

46.694

exponent	prime factors	composite factor	digits	bits*
1468963	794664191843452484127491471 3085683995023346665933859543	24520825781895036352317615281874398700333081538444 57753	55	180.678

exponent

prime factors

composite factor

digits

bits*

1468963

794664191843452484127491471
3085683995023346665933859543

24520825781895036352317615281874398700333081538444
57753

180.678

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	270000		-		-	-	0.002	-	-	0.962%
2016-03-17T19:14:44	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 794664191843452484127491471	-	-	0.071	-	-	4.936%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-09-22T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.593 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:	25.593 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
		794664191843452484127491471	1	0.00000e+0
50000	5000000		32	1.518
50000	5000000	3085683995023346665933859543	219	10.39
250000	35000000		50	13.68

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-07T21:02:00	Steve Scott	Abit	50000	5000000						3	0.142
2009-03-06T16:27:00	Sturle Sunde	FLB-ST-0034	50000	5000000						3	0.142
2009-06-06T04:49:00	axn	Manual testing			794664191843452484127491471	89.360		1		1	-
2019-04-26T10:31:11	TJAOI	Manual testing	50000	5000000	3085683995023346665933859543	91.318	219	2		219	10.39
2019-04-26T10:31:11	TJAOI	Manual testing	50000	5000000						26	1.234
2022-01-25T11:44:32	TJAOI	Manual testing	250000	35000000						50	13.68

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T04:33:40

Oliver Kruse

GTX-2

794664191843452484127491471

4B31E0C95B910E__

2017-10-28T03:35:41

Chang Chia-Tche

homura

794664191843452484127491471

4B31E0C95B910E__

2019-04-26T11:03:14

ATH

ec2-PRPCF

794664191843452484127491471

3085683995023346665933859543

3A370D491A4AFB0C

2019-04-29T02:21:26

kracker

GRID-11

794664191843452484127491471

3085683995023346665933859543

3A370D491A4AFB0C

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 = 20000, B2 = 270000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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