M1867799 Mersenne number exponent details

Residue

Status

L-L

387059B231ADC286

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	15.9085	68.6567%	500000	15000000	0.1015	5.0811%	16.0100	70.2493%	1.5926%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0284%	0.0116	64.2736%	1.1157%
GPU72	2⁶¹	0.1645	65.5738%	10000	150000	0.0014	1.6892%	0.1658	66.1553%	0.5815%
Difference	+6	+15.7441	+3.0829%	+490000	+14850000	+0.1001	+3.3918%	+15.8441	+4.0940%	+4.0940%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9085

68.6567%

500000

15000000

0.1015

5.0811%

16.0100

70.2493%

1.5926%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0284%

0.0116

64.2736%

1.1157%

GPU72

2⁶¹

0.1645

65.5738%

10000

150000

0.0014

1.6892%

0.1658

66.1553%

0.5815%

Difference

+15.7441

+3.0829%

+490000

+14850000

+0.1001

+3.3918%

+15.8441

+4.0940%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1867799	76091679059461565657	20	66.044	20369343558772 2² × 13 × 67 × 5846539483	2015-06-20	67	5846539483	9.867	25.057	46.799

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1867799

76091679059461565657

66.044

20369343558772
2² × 13 × 67 × 5846539483

2015-06-20

5846539483

9.867

25.057

46.799

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2012-01-08T15:23:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.927%
2016-03-16T12:37:42	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.081%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2012-01-08T15:23:00

markr

tiny

275000

6000000

0.046

-

-

3.927%

2016-03-16T12:37:42

alpertron

Manual testing

500000

15000000

0.101

-

-

5.081%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2010-04-06T01:39:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.082	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.854	-	-
2015-05-07T23:39:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.051	-	-
2015-05-07T23:39:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.000	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.236 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:	19.236 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.558	0.019%
25	50000	0.774	46.097%
30	250000	0.048	95.322%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	1.315
50000	5000000	76091679059461565657	2	0.138
50000	5270487		14	0.990
50000	6600000		208	16.24
50000	6750000		7	0.552

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-29T20:51:00	Rob_Dee	twopc	50000	5000000						1	0.069
2009-07-02T13:49:00	zampel	malissol	50000	5000000						3	0.208
2009-12-16T18:48:00	James Classen	towerofart	50000	5000000						3	0.208
2011-05-23T08:16:00	James Hintz	ryan	50000	5000000						3	0.208
2013-02-16T05:39:00	Xyzzy	J	50000	5000000						3	0.208
2013-12-06T12:07:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2014-09-02T02:47:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-06-20T08:14:00	Chang Chia-Tche	exbpc13	50000	5000000	76091679059461565657	66.044	2	2		2	0.138
2021-01-20T09:21:17	seatsea	dt	50000	5270487						7	0.495
2021-04-25T05:38:35	nordi	sweet16	50000	6750000						7	0.552
2021-07-14T09:01:51	seatsea	Manual testing	50000	5270487						7	0.495
2021-09-03T08:17:13	TJAOI	Manual testing	50000	6600000						208	16.24

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	387059B231ADC286	0.101

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

387059B231ADC286

0.101

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

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