M1622947 Mersenne number exponent details

Residue

Status

L-L

52B581CC77FCF516

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	18.3086	68.6567%	1000000	20000000	0.1318	5.6771%	18.4404	70.4361%	1.7794%
PrimeNet	2⁵⁷	0.0118	63.1579%	7000	120000	0.0009	2.5552%	0.0127	64.0993%	0.9414%
GPU72	2⁶¹	0.1893	65.5738%	6500	60000	0.0006	1.0597%	0.1899	65.9386%	0.3648%
Difference	+6	+18.1193	+3.0829%	+993500	+19940000	+0.1312	+4.6174%	+18.2505	+4.4975%	+4.4975%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.3086

68.6567%

1000000

20000000

0.1318

5.6771%

18.4404

70.4361%

1.7794%

PrimeNet

2⁵⁷

0.0118

63.1579%

7000

120000

0.0009

2.5552%

0.0127

64.0993%

0.9414%

GPU72

2⁶¹

0.1893

65.5738%

6500

60000

0.0006

1.0597%

0.1899

65.9386%

0.3648%

Difference

+18.1193

+3.0829%

+993500

+19940000

+0.1312

+4.6174%

+18.2505

+4.4975%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1622947	392994255774064000916983	24	78.379	121074272842570953 3 × 31 × 349 × 19463 × 191660983	2016-07-30	19463	191660983	39,458	0.6775	1.2632

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1622947

392994255774064000916983

78.379

121074272842570953
3 × 31 × 349 × 19463 × 191660983

2016-07-30

19463

191660983

39,458

0.6775

1.2632

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-12-01T13:12:00	BigBrother	Winston	1000000	20000000		-		-	-	0.132	-	-	5.677%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-12-01T13:12:00

BigBrother

Winston

1000000

20000000

0.132

-

-

5.677%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-07-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.071	-	-
2010-05-05T12:40:00	Architects Cubed	a3_lm	2⁶⁰	2⁶¹		-	-	0.095	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.189	-	-
2010-08-13T02:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.983	-	-
2016-02-23T16:28:41	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.605	-	-
2015-04-29T10:57:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.210	-	-
2015-04-30T14:35:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.302	-	-
2015-10-11T16:52:46	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.604	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.093 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.093 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	14.04
50000	5000000	392994255774064000916983	1	0.056

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-05T08:44:00	arnaud	TECH03	50000	5000000						3	0.168
2009-08-03T11:55:00	SubPrime	abd0	50000	5000000						3	0.168
2010-04-17T16:01:00	James Classen	towerofart	50000	5000000						3	0.168
2011-09-16T13:09:00	Lukasz Wrobel	i-1	50000	5000000						3	0.168
2013-02-24T23:22:00	Donna Noble	opt4820	50000	5000000						3	0.168
2013-11-09T13:09:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2014-05-31T04:57:00	mikr	MSI	50000	5000000						12	0.674
2016-03-27T12:36:38	Bruce	DESK3	50000	5000000						3	0.168
2016-05-07T00:23:58	Bruce	DESK3	50000	5000000						3	0.168
2016-07-30T05:28:05	Chang Chia-Tche	exbpc13	50000	5000000	392994255774064000916983	78.379	1	2		1	0.056
2019-10-28T14:12:46	TJAOI	Manual testing	50000	5000000						214	12.02

date	userid	compid	res64	spent (GHz-days)
1998-11-07T00:00:00	ANONYMOUS	v4_computers	52B581CC77FCF516	0.072
2015-06-27T00:56:00	MadPoo	Manual testing	52B581CC77FCF516	0.072

date

userid

compid

res64

spent (GHz-days)

1998-11-07T00:00:00

ANONYMOUS

v4_computers

52B581CC77FCF516

0.072

2015-06-27T00:56:00

MadPoo

Manual testing

52B581CC77FCF516

0.072

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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