M1681349 Mersenne number exponent details

Residue

Status

L-L

E96FD26F78AF5F92

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	17.6727	68.6567%	500000	15000000	0.0880	5.0171%	17.7607	70.2292%	1.5725%
PrimeNet	2⁵⁷	0.0114	63.1579%	8000	130000	0.0010	2.7256%	0.0124	64.1621%	1.0042%
GPU72	2⁶¹	0.1827	65.5738%	7000	90000	0.0008	1.2556%	0.1835	66.0060%	0.4323%
Difference	+6	+17.4900	+3.0829%	+493000	+14910000	+0.0872	+3.7614%	+17.5772	+4.2232%	+4.2232%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.6727

68.6567%

500000

15000000

0.0880

5.0171%

17.7607

70.2292%

1.5725%

PrimeNet

2⁵⁷

0.0114

63.1579%

8000

130000

0.0010

2.7256%

0.0124

64.1621%

1.0042%

GPU72

2⁶¹

0.1827

65.5738%

7000

90000

0.0008

1.2556%

0.1835

66.0060%

0.4323%

Difference

+17.4900

+3.0829%

+493000

+14910000

+0.0872

+3.7614%

+17.5772

+4.2232%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1681349	135216308559608507503639	24	76.840	40210660772870031 3² × 647 × 6905488712497	2008-06-11	647	6905488712497	17,714	25,674	47,952
1681349	35302127327415398913256583	26	84.868	10498155745004576359 96756389 × 108500904731	2020-01-27	96756389	108500904731	4,397,609	409.64	753.44

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1681349

135216308559608507503639

76.840

40210660772870031
3² × 647 × 6905488712497

2008-06-11

647

6905488712497

17,714

25,674

47,952

1681349

35302127327415398913256583

84.868

10498155745004576359
96756389 × 108500904731

2020-01-27

96756389

108500904731

4,397,609

409.64

753.44

exponent	prime factors	composite factor	digits	bits*
1681349	135216308559608507503639 35302127327415398913256583	4773423341514388208796127069664667013825213205537	49	161.708

exponent

prime factors

composite factor

digits

bits*

1681349

135216308559608507503639
35302127327415398913256583

4773423341514388208796127069664667013825213205537

161.708

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:18:39	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.017%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:18:39

alpertron

Manual testing

500000

15000000

0.088

-

-

5.017%

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:	15.259 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:	15.259 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
		135216308559608507503639	1	0.00000e+0
50000	5000000		254	15.08
50000	5000000	35302127327415398913256583	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-11T09:40:00	James Heinrich	Q6600			135216308559608507503639	76.840		1		1	-
2015-02-27T09:56:00	Richard B. Woods	Puttputt	50000	5000000						2	0.119
2020-01-22T00:14:49	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-01-27T11:05:52	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000	35302127327415398913256583	84.868	3	2	50600600959341	3	0.178
2020-02-02T20:30:00	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-03T10:38:07	TJAOI	Manual testing	50000	5000000						246	14.61

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	ANONYMOUS	v4_computers	E96FD26F78AF5F92	0.079

date

userid

compid

res64

spent (GHz-days)

1999-01-02T00:00:00

ANONYMOUS

v4_computers

E96FD26F78AF5F92

0.079

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T00:04:48

Oliver Kruse

GTX-3

135216308559608507503639

42F804FAC97272__

2017-11-10T22:55:17

kkmrkkblmbrbk

c4.xlarge

135216308559608507503639

42F804FAC97272__

2020-01-28T05:59:02

Chang Chia-Tche

homura

135216308559608507503639

35302127327415398913256583

0A5BF3794505A1CB

2020-01-29T14:47:51

Steve Potocny

Lenny7

135216308559608507503639

35302127327415398913256583

0A5BF3794505A1CB

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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