M2016919 Mersenne number exponent details

Residue

Status

L-L

1580AAFA452F6393

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	14.7323	68.6567%	640000	14080000	0.1308	5.2100%	14.8632	70.2897%	1.6330%
PrimeNet	2⁵⁸	0.0190	63.7931%	9000	150000	0.0016	2.6112%	0.0206	64.7385%	0.9454%
GPU72	2⁶²	0.3046	66.1290%	8000	120000	0.0013	1.2729%	0.3059	66.5602%	0.4311%
Difference	+5	+14.4277	+2.5277%	+632000	+13960000	+0.1295	+3.9371%	+14.5572	+3.7295%	+3.7295%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.7323

68.6567%

640000

14080000

0.1308

5.2100%

14.8632

70.2897%

1.6330%

PrimeNet

2⁵⁸

0.0190

63.7931%

9000

150000

0.0016

2.6112%

0.0206

64.7385%

0.9454%

GPU72

2⁶²

0.3046

66.1290%

8000

120000

0.0013

1.2729%

0.3059

66.5602%

0.4311%

Difference

+14.4277

+2.5277%

+632000

+13960000

+0.1295

+3.9371%

+14.5572

+3.7295%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2016919	110903443105958460239	21	66.588	27493281362801 1134503 × 24233767	2015-07-01	1134503	24233767	14.028	0.2281	0.2351

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2016919

110903443105958460239

66.588

27493281362801
1134503 × 24233767

2015-07-01

1134503

24233767

14.028

0.2281

0.2351

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%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	3000	3000		-		-	-	0.000	-	-	0.040%
2003-02-02T00:00:00	ANONYMOUS	v4_computers	30000	547500		-		-	-	0.006	-	-	1.426%
2010-12-07T03:13:00	Jocelyn Larouche	Manual testing	201691	201691		-		-	-	0.019	-	-	1.331%
2013-10-16T11:35:00	David Campeau	i5-2500k	640000	14080000		-		-	-	0.131	-	-	5.210%
2016-03-17T19:19:36	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.128%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	garyfu	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T07:16:46	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.076	-	-
2009-01-02T20:46:00	Sturle Sunde	doak.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-02-03T19:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.152	-	-
2013-06-06T07:18:00	David Campeau	Manual testing	2⁶²	2⁶³		-	-	0.487	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.973	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.853	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.625 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:	2.625 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.090	91.358%
30	250000	0.006	99.445%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.455
50000	5000000	110903443105958460239	2	0.169

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-02T18:20:00	Matt	Dell	50000	5000000						3	0.254
2009-09-07T17:15:00	JimBa	E5400	50000	5000000						3	0.254
2011-02-07T23:59:00	BlackburnCode	SpecOpUs2	50000	5000000						3	0.254
2013-02-04T13:50:00	butera	CSAct	50000	5000000						3	0.254
2014-03-21T08:41:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-01T04:38:00	guru	w6	50000	5000000	110903443105958460239	66.588	2	2		2	0.169
2021-09-26T09:57:43	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.593
2022-01-30T22:34:51	MarkS	desktop-i7	50000	5000000						7	0.593

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	garyfu	v4_computers	1580AAFA452F6393	0.133

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

garyfu

v4_computers

1580AAFA452F6393

0.133

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T22:54:49

Oliver Kruse

GTX-0

110903443105958460239

6E9119AA98C4AA__

2017-11-13T21:28:41

kkmrkkblmbrbk

c4.xlarge

110903443105958460239

6E9119AA98C4AA__

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 = 640000, B2 = 14080000 (P-1 stage 2)

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

B1 = 640000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 201691 (P-1 stage 1)

B1 = 30000, B2 = 547500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 3000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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