M2266493 Mersenne number exponent details

Residue

Status

L-L

1FC65386435E0DC0

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	13.1101	67.1642%	447897	16252102	0.1248	5.2084%	13.2349	68.8744%	1.7102%
PrimeNet	2⁵⁸	0.0169	62.0690%	10000	190000	0.0019	2.9201%	0.0188	63.1766%	1.1076%
GPU72	2⁶²	0.2711	64.5161%	12000	190000	0.0021	1.7072%	0.2731	65.1219%	0.6058%
Difference	+5	+12.8390	+2.6481%	+435897	+16062102	+0.1227	+3.5012%	+12.9617	+3.7525%	+3.7525%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.1101

67.1642%

447897

16252102

0.1248

5.2084%

13.2349

68.8744%

1.7102%

PrimeNet

2⁵⁸

0.0169

62.0690%

10000

190000

0.0019

2.9201%

0.0188

63.1766%

1.1076%

GPU72

2⁶²

0.2711

64.5161%

12000

190000

0.0021

1.7072%

0.2731

65.1219%

0.6058%

Difference

+12.8390

+2.6481%

+435897

+16062102

+0.1227

+3.5012%

+12.9617

+3.7525%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2266493	23736270100953847542151	23	74.330	5236343130323775 3 × 5² × 89003 × 784444439	2017-12-24	89003	784444439	2,000.4	4.0826	7.6102

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2266493

23736270100953847542151

74.330

5236343130323775
3 × 5² × 89003 × 784444439

2017-12-24

89003

784444439

2,000.4

4.0826

7.6102

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2010-11-06T12:26:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.240%
2010-11-12T22:13:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.422%
2011-01-03T16:25:00	markr	tiny	100000	2100000		-		-	-	0.020	-	-	2.716%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	128319	128319		-		-	-	0.012	-	-	1.071%
2016-04-02T11:41:48	Jocelyn Larouche	Manual testing	311040	311040		-		-	-	0.030	-	-	1.671%
2016-04-02T11:41:51	Jocelyn Larouche	Manual testing	373248	3732480	6	-		-	-	0.053	-	-	3.769%
2016-04-10T12:11:16	Jocelyn Larouche	Manual testing	447897	16252102	12	-		-	-	0.125	-	-	5.208%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:10	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.051	-	-
2009-01-10T22:50:00	Sturle Sunde	interavia.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-05T19:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.136	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.433	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.866	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.649	-	-
2015-10-31T16:44:10	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.297	-	-
2017-01-16T00:47:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.594	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.664 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	2.664 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.090	91.358%
30	250000	0.006	99.445%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.579
50000	5000000	23736270100953847542151	1	0.086

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-27T04:58:00	James Heinrich	WHS	50000	5000000						3	0.258
2010-01-01T12:27:00	James Classen	towerofart	50000	5000000						3	0.258
2011-10-30T18:20:00	Bud	annan	50000	5000000						3	0.258
2013-08-23T02:13:00	arnaud	srv-630	50000	5000000						3	0.258
2015-04-05T07:43:00	Jason U	Server7	50000	5000000						3	0.258
2016-02-06T10:26:11	Jason U	Server7	50000	5000000						3	0.258
2016-04-03T22:00:00	Bruce	Desk6	50000	5000000						3	0.258
2016-07-24T00:59:51	Bruce	Desk6	50000	5000000						3	0.258
2016-12-10T21:54:43	Bruce	Desk6	50000	5000000						3	0.258
2017-07-12T17:46:45	Bruce	Desk6	50000	5000000						3	0.258
2017-12-24T08:25:22	Bruce	Desk6	50000	5000000	23736270100953847542151	74.330	1	2		1	0.086

date	userid	compid	res64	spent (GHz-days)
1999-08-07T00:00:00	ANONYMOUS	v4_computers	1FC65386435E0DC0	0.149

date

userid

compid

res64

spent (GHz-days)

1999-08-07T00:00:00

ANONYMOUS

v4_computers

1FC65386435E0DC0

0.149

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 = 447897, B2 = 16252102 (P-1 stage 2)

B1 = 373248, B2 = 3732480 (P-1 stage 2)

B1 = 447897 (P-1 stage 1)

B1 = 373248 (P-1 stage 1)

B1 = 311040 (P-1 stage 1)

B1 = 100000, B2 = 2100000 (P-1 stage 2)

B1 = 128319 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (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