M1924969 Mersenne number exponent details

Residue

Status

L-L

D2F8B3527EA54A29

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	15.4360	68.6567%	1000000	30000000	0.2029	6.2269%	15.6390	70.6084%	1.9517%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0943%	0.0114	64.2979%	1.1400%
GPU72	2⁶¹	0.1596	65.5738%	11000	170000	0.0015	1.8139%	0.1611	66.1982%	0.6244%
Difference	+6	+15.2765	+3.0829%	+989000	+29830000	+0.2014	+4.4130%	+15.4779	+4.4102%	+4.4102%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.4360

68.6567%

1000000

30000000

0.2029

6.2269%

15.6390

70.6084%

1.9517%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0943%

0.0114

64.2979%

1.1400%

GPU72

2⁶¹

0.1596

65.5738%

11000

170000

0.0015

1.8139%

0.1611

66.1982%

0.6244%

Difference

+15.2765

+3.0829%

+989000

+29830000

+0.2014

+4.4130%

+15.4779

+4.4102%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1924969	47908018444421046306319	23	75.343	12443841548726511 3 × 7 × 11 × 4729 × 11391297089	2017-12-20	4729	11391297089	4,173.8	48.821	91.183

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1924969

47908018444421046306319

75.343

12443841548726511
3 × 7 × 11 × 4729 × 11391297089

2017-12-20

4729

11391297089

4,173.8

48.821

91.183

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-09-29T18:07:00	kurly	hex	1000000	30000000		-		-	-	0.203	-	-	6.227%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-09-29T18:07:00

kurly

hex

1000000

30000000

0.203

-

-

6.227%

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	-	-
2009-06-05T17:45:00	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		-	-	0.829	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.510	-	-
2015-05-17T18:51:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.020	-	-
2015-05-17T18:51:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	1.941	-	-
2015-09-03T11:06:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.882	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.394 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:	20.394 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.829	0.015%
25	50000	0.785	45.631%
30	250000	0.049	95.252%
35	1000000	0.002	99.776%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	2.501
50000	5000000	47908018444421046306319	3	0.208
50000	7500000		212	17.68

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-15T06:06:00	Matt	Dell	50000	5000000						3	0.208
2009-08-04T17:55:00	SubPrime	abd0	50000	5000000						3	0.208
2010-12-10T23:36:00	Lupo	yorick	50000	5000000						3	0.208
2012-11-11T12:17:00	Donna Noble	PH2x6	50000	5000000						3	0.208
2013-12-05T09:34:00	arnaud	srv-630	50000	5000000						3	0.208
2015-03-03T12:49:00	Sara	Sara	50000	5000000						3	0.208
2015-09-20T12:10:00	Chris Smith	starcraft2	50000	5000000						3	0.208
2016-03-09T20:08:55	Bruce	Desk6	50000	5000000						3	0.208
2016-06-19T05:49:46	Bruce	test	50000	5000000						3	0.208
2016-09-02T04:39:21	Bruce	test	50000	5000000						3	0.208
2017-02-15T19:14:02	Bruce	Desk6	50000	5000000						3	0.208
2017-08-10T23:27:13	Bruce	Desk6	50000	5000000						3	0.208
2017-12-20T19:49:28	Bruce	Desk6	50000	5000000	47908018444421046306319	75.343	3	2		3	0.208
2022-02-17T11:38:23	TJAOI	Manual testing	50000	7500000						212	17.68

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	D2F8B3527EA54A29	0.104
2015-07-14T15:04:00	MadPoo	Manual testing	D2F8B3527EA54A29	0.104

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

D2F8B3527EA54A29

0.104

2015-07-14T15:04:00

MadPoo

Manual testing

D2F8B3527EA54A29

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)

10²

10³

10⁴

10⁵

10⁶

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