M2793563 Mersenne number exponent details

Residue

Status

L-L

ABD404F0FF457FEB

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	10.6366	67.1642%	400000	4000000	0.0668	3.9640%	10.7033	68.4658%	1.3016%
PrimeNet	2⁵⁹	0.0275	62.7119%	12000	240000	0.0027	2.9259%	0.0302	63.8029%	1.0910%
GPU72	2⁶³	0.5713	65.0794%	15000	260000	0.0032	1.7890%	0.5745	65.7041%	0.6247%
Difference	+4	+10.0652	+2.0848%	+385000	+3740000	+0.0636	+2.1751%	+10.1288	+2.7617%	+2.7617%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.6366

67.1642%

400000

4000000

0.0668

3.9640%

10.7033

68.4658%

1.3016%

PrimeNet

2⁵⁹

0.0275

62.7119%

12000

240000

0.0027

2.9259%

0.0302

63.8029%

1.0910%

GPU72

2⁶³

0.5713

65.0794%

15000

260000

0.0032

1.7890%

0.5745

65.7041%

0.6247%

Difference

+10.0652

+2.0848%

+385000

+3740000

+0.0636

+2.1751%

+10.1288

+2.7617%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2793563	25698383040662730505487	23	74.444	4599571056865861 474169 × 9700277869	2018-01-20	474169	9700277869	2,419.3	59.238	110.55

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2793563

25698383040662730505487

74.444

4599571056865861
474169 × 9700277869

2018-01-20

474169

9700277869

2,419.3

59.238

110.55

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.300%
2010-11-14T17:34:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.253%
2010-11-22T15:18:00	markr	tiny	100000	2075000		-		-	-	0.023	-	-	2.795%
2014-11-03T03:43:00	Jocelyn Larouche	Manual testing	122976	122976		-		-	-	0.014	-	-	1.086%
2016-05-07T02:42:11	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.043	-	-	3.550%
2017-07-30T01:18:50	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.067	-	-	3.964%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:21	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-02-14T04:50:00	Sturle Sunde	gofy.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-07T12:56:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.351	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.703	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.337	-	-
2016-02-09T10:41:51	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.675	-	-
2017-10-19T22:32:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.350	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.812 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	2.812 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.499
50000	5000000	25698383040662730505487	3	0.312

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-20T11:26:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.312
2010-11-02T17:43:00	James Hintz	lappy	50000	5000000						3	0.312
2013-03-18T13:48:00	Donna Noble	PH2x6	50000	5000000						3	0.312
2015-03-21T01:51:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-16T16:34:31	Sintax	cloud	50000	5000000						3	0.312
2016-05-27T17:02:34	lettp	Home	50000	5000000						3	0.312
2017-02-08T18:35:12	Bruce	eleven	50000	5000000						3	0.312
2017-08-19T18:34:00	Marius Zens	KBWR_TV3	50000	5000000						3	0.312
2018-01-20T21:51:37	Chang Chia-Tche	ex-ctcpc	50000	5000000	25698383040662730505487	74.444	3	2		3	0.312

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	ABD404F0FF457FEB	0.216

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

ANONYMOUS

v4_computers

ABD404F0FF457FEB

0.216

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 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2075000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 122976 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000 (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

10⁹

10¹⁰

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