M2305463 Mersenne number exponent details

Residue

Status

L-L

E75EE2D8C2061AA8

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	12.8885	67.1642%	5000000	505000000	3.1582	10.9726%	16.0467	70.7671%	3.6030%
PrimeNet	2⁵⁸	0.0167	62.0690%	10000	190000	0.0019	2.9293%	0.0186	63.1801%	1.1111%
GPU72	2⁶²	0.2665	64.5161%	12000	200000	0.0022	1.7383%	0.2687	65.1330%	0.6168%
Difference	+5	+12.6220	+2.6481%	+4988000	+504800000	+3.1560	+9.2343%	+15.7780	+5.6342%	+5.6342%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.8885

67.1642%

5000000

505000000

3.1582

10.9726%

16.0467

70.7671%

3.6030%

PrimeNet

2⁵⁸

0.0167

62.0690%

10000

190000

0.0019

2.9293%

0.0186

63.1801%

1.1111%

GPU72

2⁶²

0.2665

64.5161%

12000

200000

0.0022

1.7383%

0.2687

65.1330%

0.6168%

Difference

+12.6220

+2.6481%

+4988000

+504800000

+3.1560

+9.2343%

+15.7780

+5.6342%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2305463	7325414589704669384426281	25	82.599	1588707905896704780 2² × 3² × 5 × 11 × 61 × 367 × 35841235103	2017-01-10	367	35841235103	789,000	191.28	357.26

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2305463

7325414589704669384426281

82.599

1588707905896704780
2² × 3² × 5 × 11 × 61 × 367 × 35841235103

2017-01-10

367

35841235103

789,000

191.28

357.26

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.284%
2010-02-12T10:20:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.821%
2018-02-18T19:06:17	alpertron	Manual testing	500000	15000000	12	-		-	-	0.126	-	-	5.211%
2021-06-11T03:08:41	ViliamF	3	5000000	505000000		-		-	-	3.158	-	-	10.973%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-16T01:30:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-13T12:23:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-12-06T02:47:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.426	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.852	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.621	-	-
2015-10-22T10:17:23	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.241	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.301 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	2.301 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	0.839	43.227%
25	50000	0.076	92.700%
30	250000	0.005	99.534%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.124
50000	5000000	7325414589704669384426281	2	0.177

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-17T07:17:00	oodaira	Win02	50000	5000000						3	0.266
2010-01-10T10:06:00	James Classen	towerofart	50000	5000000						3	0.266
2011-11-25T08:00:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.266
2013-09-30T12:21:00	Bruce	apandya-DESK11	50000	5000000						3	0.266
2015-04-14T20:45:00	Jason U	Server7	50000	5000000						3	0.266
2016-02-14T18:17:19	Sintax	cloud2	50000	5000000						3	0.266
2016-04-20T02:49:14	Bruce	Desk6	50000	5000000						3	0.266
2016-08-08T02:59:01	Bruce	Desk6	50000	5000000						3	0.266
2017-01-10T20:38:20	Bruce	Desk6	50000	5000000	7325414589704669384426281	82.599	2	2		2	0.177

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	E75EE2D8C2061AA8	0.156

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

E75EE2D8C2061AA8

0.156

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 = 5000000, B2 = 505000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

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

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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