M1867211 Mersenne number exponent details

Residue

Status

L-L

46EEB585A6ECEC5A

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	15.9135	68.6567%	500000	15000000	0.1015	5.0809%	16.0150	70.2492%	1.5925%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0283%	0.0116	64.2736%	1.1157%
GPU72	2⁶¹	0.1645	65.5738%	10000	150000	0.0014	1.6891%	0.1659	66.1553%	0.5815%
Difference	+6	+15.7490	+3.0829%	+490000	+14850000	+0.1001	+3.3918%	+15.8491	+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

15.9135

68.6567%

500000

15000000

0.1015

5.0809%

16.0150

70.2492%

1.5925%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0283%

0.0116

64.2736%

1.1157%

GPU72

2⁶¹

0.1645

65.5738%

10000

150000

0.0014

1.6891%

0.1659

66.1553%

0.5815%

Difference

+15.7490

+3.0829%

+490000

+14850000

+0.1001

+3.3918%

+15.8491

+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
1867211	1143646560703458585002689	25	79.920	306244597076457504 2⁵ × 3 × 3190047886213099	2015-11-15	32	3190047886213099	101,676	13,671,748	25,535,017

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1867211

1143646560703458585002689

79.920

306244597076457504
2⁵ × 3 × 3190047886213099

2015-11-15

3190047886213099

101,676

13,671,748

25,535,017

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2012-01-08T08:25:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.927%
2015-10-07T13:37:42	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	5.081%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2012-01-08T08:25:00

markr

tiny

275000

6000000

0.046

-

-

3.927%

2015-10-07T13:37:42

Bruno Victal

5820K-linux

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	-	-
2010-04-07T01:12:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.082	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.855	-	-
2015-05-07T23:39:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.051	-	-
2015-05-07T23:39:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.001	-	-
2015-09-10T11:33:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.002	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.752 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	19.752 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.782	0.015%
25	50000	0.796	45.119%
30	250000	0.049	95.196%
35	1000000	0.002	99.774%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		35	2.423
50000	5000000	1143646560703458585002689	1	0.069
50000	6600000		214	16.71
50000	6750000		7	0.552

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-26T12:13:00	LookAS	Q9550	50000	5000000						3	0.208
2009-07-23T19:59:00	KAMCOBILL	PC01	50000	5000000						3	0.208
2011-03-13T16:25:00	James Hintz	ryan	50000	5000000						3	0.208
2012-09-03T20:26:00	Bud	annan	50000	5000000						3	0.208
2013-09-28T07:01:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2014-06-14T22:07:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-03-23T02:03:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-11-15T19:12:07	Chang Chia-Tche	exbpc13	50000	5000000	1143646560703458585002689	79.920	1	2		1	0.069
2021-03-26T07:39:50	Chang Chia-Tche	exbpc13	50000	5000000						7	0.485
2021-05-03T19:33:49	nordi	sweet16	50000	6750000						7	0.552
2021-08-18T09:08:46	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.485
2021-08-20T12:37:23	TJAOI	Manual testing	50000	6600000						214	16.71

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	46EEB585A6ECEC5A	0.101
2015-06-29T14:43:00	MadPoo	Manual testing	46EEB585A6ECEC5A	0.101

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

46EEB585A6ECEC5A

0.101

2015-06-29T14:43:00

MadPoo

Manual testing

46EEB585A6ECEC5A

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

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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