M1736389 Mersenne number exponent details

Residue

Status

L-L

104C2E959A033CA4

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	17.1125	68.6567%	500000	15000000	0.1015	5.0366%	17.2140	70.2354%	1.5786%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7983%	0.0123	64.1889%	1.0310%
GPU72	2⁶¹	0.1769	65.5738%	8000	110000	0.0011	1.4104%	0.1780	66.0593%	0.4855%
Difference	+6	+16.9356	+3.0829%	+492000	+14890000	+0.1004	+3.6262%	+17.0360	+4.1760%	+4.1760%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.1125

68.6567%

500000

15000000

0.1015

5.0366%

17.2140

70.2354%

1.5786%

PrimeNet

2⁵⁷

0.0111

63.1579%

8000

140000

0.0012

2.7983%

0.0123

64.1889%

1.0310%

GPU72

2⁶¹

0.1769

65.5738%

8000

110000

0.0011

1.4104%

0.1780

66.0593%

0.4855%

Difference

+16.9356

+3.0829%

+492000

+14890000

+0.1004

+3.6262%

+17.0360

+4.1760%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1736389	35040786138427011353	20	64.926	10090131341084 2² × 2522532835271	2008-07-14	4	2522532835271	3.7471	10,811	20,192
1736389	945153400207881549875017	24	79.645	272160616143007572 2² × 3 × 73 × 310685634866447	2020-06-01	73	310685634866447	89,008	1,331,521	2,486,910

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1736389

35040786138427011353

64.926

10090131341084
2² × 2522532835271

2008-07-14

2522532835271

3.7471

10,811

20,192

1736389

945153400207881549875017

79.645

272160616143007572
2² × 3 × 73 × 310685634866447

2020-06-01

310685634866447

89,008

1,331,521

2,486,910

exponent	prime factors	composite factor	digits	bits*
1736389	35040786138427011353 945153400207881549875017	33118918164691493363421769307990213990068001	44	144.571

exponent

prime factors

composite factor

digits

bits*

1736389

35040786138427011353
945153400207881549875017

33118918164691493363421769307990213990068001

144.571

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:33:43	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.037%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:33:43

alpertron

Manual testing

500000

15000000

0.101

-

-

5.037%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-02-02T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.022

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.649 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:	17.649 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
		35040786138427011353	1	0.00000e+0
50000	5000000		156	10.71
50000	5000000	945153400207881549875017	101	6.936

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-14T22:17:00	James Heinrich	Q6600			35040786138427011353	64.926		1		1	-
2015-03-09T12:30:00	Richard B. Woods	Puttputt	50000	5000000						2	0.137
2020-02-11T22:29:59	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-19T21:10:15	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-28T00:27:50	kracker	O0	50000	5000000						3	0.206
2020-03-09T14:36:24	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-22T17:12:01	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-30T07:10:08	Greg	azure4	50000	5000000						3	0.206
2020-05-22T14:27:26	nordi	sweet16	50000	5000000						3	0.206
2020-06-01T14:17:33	TJAOI	Manual testing	50000	5000000	945153400207881549875017	79.645	101	2		101	6.936
2020-06-01T14:17:33	TJAOI	Manual testing	50000	5000000						133	9.133

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	macwang	v4_computers	104C2E959A033CA4	0.094

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

macwang

v4_computers

104C2E959A033CA4

0.094

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:16:09

alpertron

Manual testing

35040786138427011353

3B4E8D4DD08B4B__

2017-10-19T11:02:48

Oliver Kruse

Threadripper

35040786138427011353

3B4E8D4DD08B4B__

2020-06-01T15:35:37

ATH

ec2-PRPCF

35040786138427011353

945153400207881549875017

7DB0541EAFBC1558

2020-06-02T14:00:11

marssystems

SYSTEM01

35040786138427011353

945153400207881549875017

7DB0541EAFBC1558

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

10¹³

10¹⁴

10¹⁵

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