M1704067 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	17.4371	68.6567%	3000000	273000000	1.2086	9.5062%	18.6456	71.6363%	2.9796%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7325%	0.0123	64.1646%	1.0067%
GPU72	2⁶¹	0.1803	65.5738%	7000	100000	0.0008	1.3020%	0.1811	66.0220%	0.4482%
Difference	+6	+17.2568	+3.0829%	+2993000	+272900000	+1.2077	+8.2042%	+18.4645	+5.6143%	+5.6143%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.4371

68.6567%

3000000

273000000

1.2086

9.5062%

18.6456

71.6363%

2.9796%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7325%

0.0123

64.1646%

1.0067%

GPU72

2⁶¹

0.1803

65.5738%

7000

100000

0.0008

1.3020%

0.1811

66.0220%

0.4482%

Difference

+17.2568

+3.0829%

+2993000

+272900000

+1.2077

+8.2042%

+18.4645

+5.6143%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1704067	128721813047	12	36.905	37769 179 × 211	-	179	211	6.313e-9	1.233e-5	2.486e-5
1704067	332123448987089	15	48.239	97450232 2³ × 11 × 1107389	2008-08-26	11	1107389	2.473e-5	0.0041	0.0077

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1704067

128721813047

36.905

37769
179 × 211

179

211

6.313e-9

1.233e-5

2.486e-5

1704067

332123448987089

48.239

97450232
2³ × 11 × 1107389

2008-08-26

1107389

2.473e-5

0.0041

0.0077

exponent	prime factors	composite factor	digits	bits*
1704067	128721813047 332123448987089	42751532509040911774750183	26	85.144

exponent

prime factors

composite factor

digits

bits*

1704067

128721813047
332123448987089

42751532509040911774750183

85.144

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:29:38	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 128721813047 skipped known factor: 332123448987089	-	-	0.088	-	-	5.025%
2021-07-16T12:52:32	Dylan Delgado	laptop-ryzen73700	3000000	273000000		-	skipped known factor: 128721813047 skipped known factor: 332123448987089	-	-	1.209	-	-	9.506%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26T20:19:00	ANONYMOUS	Manual testing	?	?	332123448987089	48.239	15	2.72440e-6	0.174	5.92001e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.280 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:	15.280 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	9.885	0.005%
25	50000	0.915	40.068%
30	250000	0.058	94.394%
35	1000000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	15.28

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-05-17T04:41:42	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-06T17:52:13	Gordon Spence	haswell	50000	5000000						3	0.178
2019-05-07T21:37:46	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-02-02T21:07:10	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-10T05:39:47	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-03-03T14:21:42	TJAOI	Manual testing	50000	5000000						244	14.51

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:15:09

alpertron

Manual testing

128721813047

332123448987089

C43BEC1FD4D661__

2017-10-18T19:16:38

Oliver Kruse

Threadripper

128721813047

332123448987089

C43BEC1FD4D661__

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 = 3000000, B2 = 273000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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