M2097829 Mersenne number exponent details

Residue

Status

L-L

D358480C83162938

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	14.1641	67.1642%	500000	15000000	0.1230	5.1525%	14.2871	68.8561%	1.6919%
PrimeNet	2⁵⁸	0.0183	62.0690%	9000	160000	0.0016	2.6772%	0.0199	63.0845%	1.0155%
GPU72	2⁶²	0.2929	64.5161%	9000	140000	0.0015	1.4014%	0.2944	65.0134%	0.4973%
Difference	+5	+13.8713	+2.6481%	+491000	+14860000	+0.1214	+3.7512%	+13.9927	+3.8427%	+3.8427%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.1641

67.1642%

500000

15000000

0.1230

5.1525%

14.2871

68.8561%

1.6919%

PrimeNet

2⁵⁸

0.0183

62.0690%

9000

160000

0.0016

2.6772%

0.0199

63.0845%

1.0155%

GPU72

2⁶²

0.2929

64.5161%

9000

140000

0.0015

1.4014%

0.2944

65.0134%

0.4973%

Difference

+13.8713

+2.6481%

+491000

+14860000

+0.1214

+3.7512%

+13.9927

+3.8427%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2097829	27694718875279667297	20	64.586	6600804659312 2⁴ × 412943 × 999049	2009-11-08	412943	999049	2.1485	0.0424	0.0801

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2097829

27694718875279667297

64.586

6600804659312
2⁴ × 412943 × 999049

2009-11-08

412943

999049

2.1485

0.0424

0.0801

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2009-07-31T22:12:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.020%
2016-03-16T13:44:34	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 27694718875279667297	-	-	0.123	-	-	5.153%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-29T00:00:00	Charlie Dorian	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T08:46:54	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.073	-	-
2009-01-03T09:09:00	Sturle Sunde	nouchcraft.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.808 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:	2.808 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.237	29.020%
25	50000	0.114	89.195%
30	250000	0.007	99.278%

ECM Summary

B1	B2	factor	curves	GHz-days
		27694718875279667297	1	0.00000e+0
50000	5000000		17	1.446
50000	6750000		14	1.361

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-08T02:13:00	Martti Järvi	SKYNET	50000	5000000						3	0.255
2009-11-08T14:03:00	KAMCOBILL	PC01			27694718875279667297	64.586		1		1	-
2021-09-16T20:54:32	Dylan Delgado	colab	50000	6750000						7	0.681
2022-01-20T20:50:48	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.596
2022-05-19T17:03:10	Dylan Delgado	colab	50000	6750000						7	0.681
2022-07-17T03:24:48	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.596

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-08T00:00:00	ANONYMOUS	v4_computers	D358480C83162938	0.138
1999-01-29T00:00:00	Charlie Dorian	v4_computers	D358480C83162938	0.138

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T23:48:57

Oliver Kruse

GTX-0

27694718875279667297

F0E299F281AF4D__

2017-11-17T01:50:53

kkmrkkblmbrbk

c4.xlarge

27694718875279667297

F0E299F281AF4D__

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 = 260000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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