M1923073 Mersenne number exponent details

Residue

Status

L-L

DCD4A50670DD7488

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	15.4513	68.6567%	1000000	30000000	0.2029	6.2262%	15.6542	70.6082%	1.9515%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0937%	0.0114	64.2977%	1.1398%
GPU72	2⁶¹	0.1597	65.5738%	10000	170000	0.0015	1.7621%	0.1612	66.1804%	0.6066%
Difference	+6	+15.2915	+3.0829%	+990000	+29830000	+0.2015	+4.4641%	+15.4930	+4.4278%	+4.4278%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.4513

68.6567%

1000000

30000000

0.2029

6.2262%

15.6542

70.6082%

1.9515%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0937%

0.0114

64.2977%

1.1398%

GPU72

2⁶¹

0.1597

65.5738%

10000

170000

0.0015

1.7621%

0.1612

66.1804%

0.6066%

Difference

+15.2915

+3.0829%

+990000

+29830000

+0.2015

+4.4641%

+15.4930

+4.4278%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1923073	33006481003395854559361	23	74.805	8581702567556160 2⁶ × 3² × 5 × 7 × 425679690851	2017-02-13	64	425679690851	3,798.1	1,824.4	3,407.4

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1923073

33006481003395854559361

74.805

8581702567556160
2⁶ × 3² × 5 × 7 × 425679690851

2017-02-13

425679690851

3,798.1

1,824.4

3,407.4

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-09-27T05:48:00	kurly	hex	1000000	30000000		-		-	-	0.203	-	-	6.226%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-09-27T05:48:00

kurly

hex

1000000

30000000

0.203

-

-

6.226%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-12-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.060	-	-
2009-06-04T13:34:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.080	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.160	-	-
2011-08-27T22:20:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.830	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.510	-	-
2015-05-17T10:45:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.021	-	-
2015-05-17T10:45:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	1.943	-	-
2015-09-03T11:06:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.886	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.317 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	19.317 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.549	0.019%
25	50000	0.775	46.079%
30	250000	0.048	95.319%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.084
50000	5000000	33006481003395854559361	2	0.139
50000	6600000		211	16.54
50000	6750000		7	0.555

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-09T20:44:00	Jorge Flora	PC_PN03	50000	5000000						3	0.208
2009-08-04T00:10:00	SubPrime	abd0	50000	5000000						3	0.208
2010-12-09T19:15:00	Lupo	yorick	50000	5000000						3	0.208
2012-11-09T11:33:00	Donna Noble	PH2x6	50000	5000000						3	0.208
2013-12-03T20:47:00	arnaud	srv-630	50000	5000000						3	0.208
2015-02-16T18:50:00	Sara	Sara	50000	5000000						3	0.208
2015-10-02T20:27:27	Sara	Sara	50000	5000000						3	0.208
2016-03-09T01:12:31	Bruce	Desk6	50000	5000000						3	0.208
2016-06-18T13:44:21	Bruce	test	50000	5000000						3	0.208
2016-08-31T06:09:44	Bruce	test	50000	5000000						3	0.208
2017-02-13T18:03:19	Bruce	Desk6	50000	5000000	33006481003395854559361	74.805	2	2		2	0.139
2021-10-03T08:21:18	Dylan Delgado	laptop-ryzen73700	50000	6750000						7	0.555
2022-02-03T11:49:00	TJAOI	Manual testing	50000	6600000						211	16.54

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	DCD4A50670DD7488	0.104
2015-06-28T05:06:00	MadPoo	Manual testing	DCD4A50670DD7488	0.104

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

DCD4A50670DD7488

0.104

2015-06-28T05:06:00

MadPoo

Manual testing

DCD4A50670DD7488

0.104

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 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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