M1718701 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	17.2886	68.6567%	500000	15000000	0.0880	5.0304%	17.3766	70.2334%	1.5767%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7929%	0.0122	64.1869%	1.0290%
GPU72	2⁶¹	0.1787	65.5738%	7000	110000	0.0009	1.3434%	0.1796	66.0363%	0.4625%
Difference	+6	+17.1099	+3.0829%	+493000	+14890000	+0.0872	+3.6869%	+17.1970	+4.1971%	+4.1971%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.2886

68.6567%

500000

15000000

0.0880

5.0304%

17.3766

70.2334%

1.5767%

PrimeNet

2⁵⁷

0.0112

63.1579%

8000

140000

0.0010

2.7929%

0.0122

64.1869%

1.0290%

GPU72

2⁶¹

0.1787

65.5738%

7000

110000

0.0009

1.3434%

0.1796

66.0363%

0.4625%

Difference

+17.1099

+3.0829%

+493000

+14890000

+0.0872

+3.6869%

+17.1970

+4.1971%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1718701	10312207	8	23.298	3 3	-	1	3	6.506e-13	7.568e-8	1.389e-7
1718701	174529731076646938367	21	67.242	50773732917083 11 × 723959 × 6375767	2019-05-27	723959	6375767	32.734	0.0704	0.1005
1718701	326554844439522401039	21	68.146	95000481305219 7 × 59 × 230025378463	2020-05-04	59	230025378463	48.225	855.22	1,597.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1718701

10312207

23.298

3
3

6.506e-13

7.568e-8

1.389e-7

1718701

174529731076646938367

67.242

50773732917083
11 × 723959 × 6375767

2019-05-27

723959

6375767

32.734

0.0704

0.1005

1718701

326554844439522401039

68.146

95000481305219
7 × 59 × 230025378463

2020-05-04

230025378463

48.225

855.22

1,597.3

exponent	prime factors	composite factor	digits	bits*
1718701	10312207 174529731076646938367	1799786714516716094356745969	28	90.540
1718701	10312207 326554844439522401039	3367501152713153980651183073	28	91.444
1718701	174529731076646938367 326554844439522401039	56993529181806119457012136640352089763313	41	135.388
1718701	10312207 174529731076646938367 326554844439522401039	587729070583325337707436754547595302521864661791	48	158.686

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:30:55	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 10312207	-	-	0.088	-	-	5.030%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:30:55

alpertron

Manual testing

500000

15000000

skipped known factor: 10312207

0.088

-

-

5.030%

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.186 GHz-days
Estimated T-Level:	24.857

Digits	B1	Curves	Complete	FacMiss
20	11000	272 / 100	2.720	6.498%
25	50000	272 / 280	0.971	37.788%

New Calculation Method

Total ECM effort:	16.186 GHz-days
Estimated T-Level:	24.857

Digits	B1	Complete	FacMiss
20	11000	8.774	0.015%
25	50000	0.793	45.248%
30	250000	0.049	95.234%
35	1000000	0.002	99.777%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		242	14.40
50000	5000000	174529731076646938367	2	0.119
50000	5000000	326554844439522401039	28	1.666

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-22T19:41:04	Richard B. Woods	Puttputt	50000	5000000						1	0.060
2018-03-12T04:23:35	Oliver Kruse	ECM-HTC	50000	5000000						3	0.179
2019-05-27T14:28:02	Chang Chia-Tche	exbpc13	50000	5000000	174529731076646938367	67.242	2	2		2	0.119
2020-02-11T14:06:37	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.179
2020-02-14T13:16:00	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-02-22T11:20:49	kracker	O0	50000	5000000						3	0.179
2020-03-01T13:27:11	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-03-13T21:09:14	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-04-20T19:25:45	Team_Inspector	SpudBoy4	50000	5000000						3	0.179
2020-05-03T12:45:18	Oliver Kruse	Melissa	50000	5000000						3	0.179
2020-05-04T10:43:33	TJAOI	Manual testing	50000	5000000	326554844439522401039	68.146	28	2		28	1.666
2020-05-04T10:43:34	TJAOI	Manual testing	50000	5000000						217	12.91

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:15:37

alpertron

Manual testing

10312207

43720E0EC52DC2__

2017-10-19T03:52:41

Oliver Kruse

GTX-1

10312207

43720E0EC52DC2__

2019-05-30T02:00:47

fre_games

gpu

10312207

174529731076646938367

C1F68B73C9E48165

2019-05-30T02:23:55

ATH

ec2-PRPCFDC

10312207

174529731076646938367

C1F68B73C9E48165

2019-05-30T22:07:50

Daniil Tsarkov

tsar1

10312207

174529731076646938367

C1F68B73C9E48165

2020-05-05T00:02:29

CrypticClue

cruncher

10312207

174529731076646938367

326554844439522401039

C1F68B73C9E48165

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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