M2170213 Mersenne number exponent details

Residue

Status

L-L

E2F9B04F4AE75BDF

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	13.6917	67.1642%	500000	15000000	0.1230	5.1736%	13.8147	68.8630%	1.6988%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8559%	0.0195	63.1522%	1.0833%
GPU72	2⁶²	0.2831	64.5161%	11000	160000	0.0018	1.5673%	0.2849	65.0723%	0.5562%
Difference	+5	+13.4086	+2.6481%	+489000	+14840000	+0.1212	+3.6063%	+13.5298	+3.7907%	+3.7907%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.6917

67.1642%

500000

15000000

0.1230

5.1736%

13.8147

68.8630%

1.6988%

PrimeNet

2⁵⁸

0.0177

62.0690%

10000

180000

0.0018

2.8559%

0.0195

63.1522%

1.0833%

GPU72

2⁶²

0.2831

64.5161%

11000

160000

0.0018

1.5673%

0.2849

65.0723%

0.5562%

Difference

+13.4086

+2.6481%

+489000

+14840000

+0.1212

+3.6063%

+13.5298

+3.7907%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2170213	14261484247244712590311	23	73.595	3285733761442935 3³ × 5 × 11² × 45377 × 4432793	2016-03-07	45377	4432793	975.85	0.0271	0.0430
2170213	5799376063194183041728759	25	82.262	1336130615564965983 3 × 7 × 3721847 × 17095078709	2009-12-03	3721847	17095078709	826,742	89.132	165.85

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2170213

14261484247244712590311

73.595

3285733761442935
3³ × 5 × 11² × 45377 × 4432793

2016-03-07

45377

4432793

975.85

0.0271

0.0430

2170213

5799376063194183041728759

82.262

1336130615564965983
3 × 7 × 3721847 × 17095078709

2009-12-03

3721847

17095078709

826,742

89.132

165.85

exponent	prime factors	composite factor	digits	bits*
2170213	14261484247244712590311 5799376063194183041728759	82707710369091898290261098286088386618353454049	47	155.857

exponent

prime factors

composite factor

digits

bits*

2170213

14261484247244712590311
5799376063194183041728759

82707710369091898290261098286088386618353454049

155.857

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.279%
2016-03-07T18:39:10	alpertron	Manual testing	500000	15000000	12		14261484247244712590311	23	73.595	0.123	0.285	0.246	5.174%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T16:35:56	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.071	-	-
2009-01-04T22:49:00	Sturle Sunde	gonzo.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-07T09:55:00	Sturle Sunde	gibsy.ifi	2⁶¹	2⁶²		-	-	0.142	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.210 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.210 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.968	37.986%
25	50000	0.089	91.464%
30	250000	0.006	99.436%

ECM Summary

B1	B2	factor	curves	GHz-days
		5799376063194183041728759	1	0.00000e+0
50000	5000000		10	0.855
50000	6499017		7	0.672
50000	6750000		7	0.684

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-19T23:53:00	paulie	iMac3.4	50000	5000000						3	0.256
2009-12-03T16:03:00	SubPrime	abd0			5799376063194183041728759	82.262		1		1	-
2022-03-10T16:52:49	Dylan Delgado	colab	50000	6750000						7	0.684
2022-06-12T07:15:58	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.598
2022-08-09T11:06:37	debrouxl	dl380g9-1	50000	6499017						7	0.672

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-04T00:00:00	ANONYMOUS	v4_computers	E2F9B04F4AE75BDF	0.143
1999-02-21T00:00:00	ANONYMOUS	v4_computers	E2F9B04F4AE75BDF	0.143

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T03:14:34

Oliver Kruse

GTX-2

14261484247244712590311

5799376063194183041728759

286CF6FD2E1AB5D3

2017-10-17T23:57:53

Oliver Kruse

GTX-0

14261484247244712590311

5799376063194183041728759

46A1B6455ED8EC__

2017-11-19T04:39:45

kkmrkkblmbrbk

c4.xlarge

14261484247244712590311

5799376063194183041728759

46A1B6455ED8EC__

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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