M2022893 Mersenne number exponent details

Residue

Status

L-L

9848D66224CD40A4

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	14.6888	68.6567%	580000	15080000	0.1306	5.2236%	14.8194	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	66.5604%	0.4314%
Difference	+5	+14.3851	+2.5277%	+572000	+14960000	+0.1293	+3.9499%	+14.5144	+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

14.6888

68.6567%

580000

15080000

0.1306

5.2236%

14.8194

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

66.5604%

0.4314%

Difference

+14.3851

+2.5277%

+572000

+14960000

+0.1293

+3.9499%

+14.5144

+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
2022893	44505148507721617223159	23	75.236	11000371375975303 7 × 37 × 42472476355117	2015-07-03	37	42472476355117	6,126.8	220,613	412,043

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2022893

44505148507721617223159

75.236

11000371375975303
7 × 37 × 42472476355117

2015-07-03

42472476355117

6,126.8

220,613

412,043

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%
2003-01-01T00:00:00	ANONYMOUS	v4_computers	25000	412500		-		-	-	0.004	-	-	1.247%
2010-12-10T00:56:00	Jocelyn Larouche	Manual testing	202289	202289		-		-	-	0.019	-	-	1.334%
2013-10-21T00:03:00	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	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T07:16:46	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.076	-	-
2009-01-02T11:56:00	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		-	-	0.971	-	-
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:	1.600

Digits	B1	Curves	Complete	FacMiss
20	11000	32 / 100	0.320	72.498%
25	50000	32 / 280	0.114	89.182%

New Calculation Method

Total ECM effort:	2.710 GHz-days
Estimated T-Level:	1.600

Digits	B1	Complete	FacMiss
20	11000	1.032	35.620%
25	50000	0.093	91.093%
30	250000	0.006	99.427%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.456
50000	5000000	44505148507721617223159	3	0.254

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-02T04:30:00	firehawk	cidnp2	50000	5000000						3	0.254
2009-09-10T21:08:00	SubPrime	mysql0	50000	5000000						3	0.254
2011-02-13T22:28:00	Lupo	yorick	50000	5000000						3	0.254
2013-02-13T23:07:00	MadPoo	IntLAVH03	50000	5000000						3	0.254
2014-03-18T10:06:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-03T06:40:00	guru	w6	50000	5000000	44505148507721617223159	75.236	3	2		3	0.254
2021-10-21T19:16:41	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.593
2022-05-10T18:46:00	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.593

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	ANONYMOUS	v4_computers	9848D66224CD40A4	0.133

date

userid

compid

res64

spent (GHz-days)

1999-05-23T00:00:00

ANONYMOUS

v4_computers

9848D66224CD40A4

0.133

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T00:52:57

Oliver Kruse

GTX-0

44505148507721617223159

F6EBA8C9934D13__

2017-11-14T03:59:12

kkmrkkblmbrbk

c4.xlarge

44505148507721617223159

F6EBA8C9934D13__

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 = 202289 (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

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