M1708229 Mersenne number exponent details

Residue

Status

L-L

EFA1A478F15ECF42

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	17.3946	68.6567%	500000	15000000	0.0880	5.0267%	17.4826	70.2322%	1.5755%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7897%	0.0123	64.1857%	1.0278%
GPU72	2⁶¹	0.1798	65.5738%	7000	100000	0.0008	1.3027%	0.1806	66.0222%	0.4485%
Difference	+6	+17.2148	+3.0829%	+493000	+14900000	+0.0872	+3.7240%	+17.3020	+4.2100%	+4.2100%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.3946

68.6567%

500000

15000000

0.0880

5.0267%

17.4826

70.2322%

1.5755%

PrimeNet

2⁵⁷

0.0112

63.1579%

8000

140000

0.0010

2.7897%

0.0123

64.1857%

1.0278%

GPU72

2⁶¹

0.1798

65.5738%

7000

100000

0.0008

1.3027%

0.1806

66.0222%

0.4485%

Difference

+17.2148

+3.0829%

+493000

+14900000

+0.0872

+3.7240%

+17.3020

+4.2100%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1708229	113171180978924469887	21	66.617	33125295548467 2293 × 14446269319	2008-06-27	2293	14446269319	12.522	53.710	100.32

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1708229

113171180978924469887

66.617

33125295548467
2293 × 14446269319

2008-06-27

2293

14446269319

12.522

53.710

100.32

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:29:59	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.027%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:29:59

alpertron

Manual testing

500000

15000000

0.088

-

-

5.027%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
1998-12-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
1998-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.938 GHz-days
Estimated T-Level:	24.786

Digits	B1	Curves	Complete	FacMiss
20	11000	268 / 100	2.680	6.764%
25	50000	268 / 280	0.957	38.333%

New Calculation Method

Total ECM effort:	15.938 GHz-days
Estimated T-Level:	24.786

Digits	B1	Complete	FacMiss
20	11000	10.308	0.003%
25	50000	0.954	38.530%
30	250000	0.060	94.162%
35	1000000	0.003	99.719%

ECM Summary

B1	B2	factor	curves	GHz-days
		113171180978924469887	1	0.00000e+0
50000	5000000		268	15.94

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-27T00:31:00	Team_Bundu	bundu4			113171180978924469887	66.617		1		1	-
2018-03-08T14:48:13	Ismo Laitela	6600K	50000	5000000						3	0.178
2019-05-13T12:49:56	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-02-04T14:15:04	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-12T07:32:41	kracker	O0	50000	5000000						3	0.178
2020-02-20T04:48:06	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-28T06:25:13	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-10T02:26:20	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-23T11:54:36	-Anonymous-	aws-nano	50000	5000000						3	0.178
2020-03-30T08:12:05	TJAOI	Manual testing	50000	5000000						244	14.51

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	EFA1A478F15ECF42	0.080
2000-04-27T00:00:00	ANONYMOUS	v4_computers	EFA1A478F15ECF42	0.080

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

EFA1A478F15ECF42

0.080

2000-04-27T00:00:00

ANONYMOUS

v4_computers

EFA1A478F15ECF42

0.080

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)

10²

10³

10⁴

10⁵

10⁶

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