M1863347 Mersenne number exponent details

Residue

Status

L-L

B14B2F84834842C8

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	15.9465	68.6567%	500000	15000000	0.1015	5.0796%	16.0480	70.2488%	1.5921%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0271%	0.0117	64.2731%	1.1153%
GPU72	2⁶¹	0.1649	65.5738%	10000	150000	0.0014	1.6884%	0.1662	66.1550%	0.5813%
Difference	+6	+15.7817	+3.0829%	+490000	+14850000	+0.1001	+3.3912%	+15.8818	+4.0938%	+4.0938%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9465

68.6567%

500000

15000000

0.1015

5.0796%

16.0480

70.2488%

1.5921%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0271%

0.0117

64.2731%

1.1153%

GPU72

2⁶¹

0.1649

65.5738%

10000

150000

0.0014

1.6884%

0.1662

66.1550%

0.5813%

Difference

+15.7817

+3.0829%

+490000

+14850000

+0.1001

+3.3912%

+15.8818

+4.0938%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1863347	3018006160481114623943	22	71.354	809834711538193 11 × 811 × 90778467833	2015-03-19	811	90778467833	343.96	389.05	726.64

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1863347

3018006160481114623943

71.354

809834711538193
11 × 811 × 90778467833

2015-03-19

811

90778467833

343.96

389.05

726.64

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2012-01-06T09:11:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.926%
2016-03-16T12:37:16	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.080%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2012-01-06T09:11:00

markr

tiny

275000

6000000

0.046

-

-

3.926%

2016-03-16T12:37:16

alpertron

Manual testing

500000

15000000

0.101

-

-

5.080%

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		-	-	0.857	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.312 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	20.312 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	9.044	0.012%
25	50000	0.819	44.073%
30	250000	0.051	95.058%
35	1000000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	2.699
50000	5000000	3018006160481114623943	3	0.208
50000	6600000		223	17.41

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-22T17:36:00	ANONYMOUS	mcg25	50000	5000000						3	0.208
2009-07-21T02:19:00	James Hintz	16_071509	50000	5000000						3	0.208
2011-03-10T03:13:00	Thomas N	ubuntu	50000	5000000						3	0.208
2012-08-27T18:56:00	Bud	annan	50000	5000000						3	0.208
2013-09-25T06:34:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2014-06-12T03:21:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-03-19T19:17:00	Chang Chia-Tche	exbpc13	50000	5000000	3018006160481114623943	71.354	3	2		3	0.208
2021-01-17T07:58:44	Chang Chia-Tche	exbpc13	50000	5000000						7	0.484
2021-04-13T22:40:52	Chang Chia-Tche	exbpc13	50000	5000000						7	0.484
2021-07-25T14:36:46	Daniil Tsarkov	9900KF	50000	5000000						7	0.484
2021-08-27T10:08:03	TJAOI	Manual testing	50000	6600000						223	17.41

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	B14B2F84834842C8	0.101

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

B14B2F84834842C8

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

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