M1678199 Mersenne number exponent details

Residue

Status

L-L

BE0D2C8EC9025EF0

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	17.7058	68.6567%	500000	15000000	0.0880	5.0159%	17.7939	70.2289%	1.5722%
PrimeNet	2⁵⁷	0.0114	63.1579%	8000	130000	0.0010	2.7246%	0.0124	64.1617%	1.0038%
GPU72	2⁶¹	0.1830	65.5738%	7000	90000	0.0008	1.2551%	0.1838	66.0059%	0.4321%
Difference	+6	+17.5228	+3.0829%	+493000	+14910000	+0.0872	+3.7608%	+17.6100	+4.2230%	+4.2230%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.7058

68.6567%

500000

15000000

0.0880

5.0159%

17.7939

70.2289%

1.5722%

PrimeNet

2⁵⁷

0.0114

63.1579%

8000

130000

0.0010

2.7246%

0.0124

64.1617%

1.0038%

GPU72

2⁶¹

0.1830

65.5738%

7000

90000

0.0008

1.2551%

0.1838

66.0059%

0.4321%

Difference

+17.5228

+3.0829%

+493000

+14910000

+0.0872

+3.7608%

+17.6100

+4.2230%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1678199	4215243210059065711	19	61.870	1255883006145 3 × 5 × 18773 × 4459891	2009-09-18	18773	4459891	0.2775	0.0178	0.0310

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1678199

4215243210059065711

61.870

1255883006145
3 × 5 × 18773 × 4459891

2009-09-18

18773

4459891

0.2775

0.0178

0.0310

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:18:17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 4215243210059065711	-	-	0.088	-	-	5.016%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.721 GHz-days
Estimated T-Level:	24.429

Digits	B1	Curves	Complete	FacMiss
20	11000	248 / 100	2.480	8.270%
25	50000	248 / 280	0.886	41.177%

New Calculation Method

Total ECM effort:	14.721 GHz-days
Estimated T-Level:	24.429

Digits	B1	Complete	FacMiss
20	11000	9.538	0.007%
25	50000	0.883	41.372%
30	250000	0.056	94.585%
35	1000000	0.003	99.740%

ECM Summary

B1	B2	factor	curves	GHz-days
		4215243210059065711	1	0.00000e+0
50000	5000000		248	14.72

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-07T13:40:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-09-18T08:58:00	SubPrime	stor			4215243210059065711	61.870		1		1	-
2020-01-06T12:25:33	TJAOI	Manual testing	50000	5000000						245	14.54

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	BE0D2C8EC9025EF0	0.079

date

userid

compid

res64

spent (GHz-days)

1998-11-21T00:00:00

ANONYMOUS

v4_computers

BE0D2C8EC9025EF0

0.079

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:23:17

alpertron

Manual testing

4215243210059065711

485A46E9912CDE__

2017-10-18T13:50:52

Oliver Kruse

Threadripper

4215243210059065711

485A46E9912CDE__

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 = 500000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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