M2023093 Mersenne number exponent details

Residue

Status

L-L

5746840A1FF68D3C

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	14.6874	68.6567%	580000	15080000	0.1306	5.2237%	14.8180	70.2940%	1.6373%
PrimeNet	2⁵⁸	0.0190	63.7931%	9000	150000	0.0016	2.6127%	0.0206	64.7391%	0.9460%
GPU72	2⁶²	0.3037	66.1290%	8000	120000	0.0013	1.2737%	0.3050	66.5605%	0.4314%
Difference	+5	+14.3837	+2.5277%	+572000	+14960000	+0.1293	+3.9500%	+14.5130	+3.7335%	+3.7335%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.6874

68.6567%

580000

15080000

0.1306

5.2237%

14.8180

70.2940%

1.6373%

PrimeNet

2⁵⁸

0.0190

63.7931%

9000

150000

0.0016

2.6127%

0.0206

64.7391%

0.9460%

GPU72

2⁶²

0.3037

66.1290%

8000

120000

0.0013

1.2737%

0.3050

66.5605%

0.4314%

Difference

+14.3837

+2.5277%

+572000

+14960000

+0.1293

+3.9500%

+14.5130

+3.7335%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2023093	1114908292065081470743	22	69.917	275545487050047 3³ × 41 × 248911912421	2015-07-03	41	248911912421	110.01	1,292.9	2,414.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2023093

1114908292065081470743

69.917

275545487050047
3³ × 41 × 248911912421

2015-07-03

248911912421

110.01

1,292.9

2,414.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.022%
2003-01-09T00:00:00	ANONYMOUS	v4_computers	25000	412500		-		-	-	0.004	-	-	1.247%
2010-12-10T00:56:00	Jocelyn Larouche	Manual testing	202309	202309		-		-	-	0.019	-	-	1.334%
2013-10-21T01:08:00	David Campeau	i5-2500k	580000	15080000		-		-	-	0.131	-	-	5.224%
2016-03-17T19:19:41	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.130%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	estrand	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T07:16:46	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.076	-	-
2009-01-02T15:01:00	Sturle Sunde	foster.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-02-05T16:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.152	-	-
2013-02-11T20:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.485	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.970	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.847	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.710 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	2.710 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.016	36.219%
25	50000	0.092	91.199%
30	250000	0.006	99.434%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	1.863
50000	5000000	1114908292065081470743	2	0.169
50000	6750000		7	0.677

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-02T16:09:00	mdrg	MDRG02	50000	5000000						3	0.254
2009-09-13T15:58:00	lindee	tanagra	50000	5000000						3	0.254
2011-02-14T05:44:00	James Hintz	ryan	50000	5000000						3	0.254
2013-02-18T07:13:00	OS1	L3	50000	5000000						3	0.254
2014-03-18T11:35:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-03T08:10:00	guru	w1	50000	5000000	1114908292065081470743	69.917	2	2		2	0.169
2021-10-05T18:02:58	happy5214	Focus	50000	6750000						7	0.677
2022-03-05T08:39:21	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.593

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	estrand	v4_computers	5746840A1FF68D3C	0.133

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

estrand

v4_computers

5746840A1FF68D3C

0.133

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T00:33:53

Oliver Kruse

GTX-3

1114908292065081470743

381BF60FD82B3D__

2017-11-19T12:47:02

kkmrkkblmbrbk

c4.xlarge

1114908292065081470743

381BF60FD82B3D__

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 = 580000, B2 = 15080000 (P-1 stage 2)

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

B1 = 580000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 202309 (P-1 stage 1)

B1 = 25000, B2 = 412500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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