M2013001 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	14.7610	68.6567%	500000	15000000	0.1230	5.1270%	14.8840	70.2637%	1.6070%
PrimeNet	2⁵⁸	0.0191	63.7931%	9000	150000	0.0016	2.6102%	0.0207	64.7382%	0.9451%
GPU72	2⁶²	0.3052	66.1290%	8000	120000	0.0013	1.2724%	0.3065	66.5600%	0.4310%
Difference	+5	+14.4558	+2.5277%	+492000	+14880000	+0.1216	+3.8547%	+14.5774	+3.7037%	+3.7037%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.7610

68.6567%

500000

15000000

0.1230

5.1270%

14.8840

70.2637%

1.6070%

PrimeNet

2⁵⁸

0.0191

63.7931%

9000

150000

0.0016

2.6102%

0.0207

64.7382%

0.9451%

GPU72

2⁶²

0.3052

66.1290%

8000

120000

0.0013

1.2724%

0.3065

66.5600%

0.4310%

Difference

+14.4558

+2.5277%

+492000

+14880000

+0.1216

+3.8547%

+14.5774

+3.7037%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2013001	3655609817	10	31.767	908 2² × 227	-	4	227	1.700e-10	1.540e-6	2.171e-6
2013001	4199120087	10	31.967	1043 7 × 149	2008-07-15	7	149	1.742e-10	1.405e-6	1.405e-6
2013001	72008588682677195212759	23	75.931	17885880007679379 3 × 5961960002559793	2019-05-18	3	5961960002559793	6,844.8	30,967,911	57,839,433

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2013001

3655609817

31.767

908
2² × 227

227

1.700e-10

1.540e-6

2.171e-6

2013001

4199120087

31.967

1043
7 × 149

2008-07-15

149

1.742e-10

1.405e-6

2013001

72008588682677195212759

75.931

17885880007679379
3 × 5961960002559793

2019-05-18

5961960002559793

6,844.8

30,967,911

57,839,433

exponent	prime factors	composite factor	digits	bits*
2013001	3655609817 4199120087	15350344612799094079	20	63.735
2013001	3655609817 72008588682677195212759	263235303696709852661787204055103	33	107.698
2013001	4199120087 72008588682677195212759	302372711173950679354716555590033	33	107.898
2013001	3655609817 4199120087 72008588682677195212759	1105356651360399698122921065867350862153961	43	139.665

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:19:32	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 3655609817 skipped known factor: 4199120087	-	-	0.123	-	-	5.127%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:49:00	J Feitsma	Manual testing	?	?	4199120087	31.967	10	3.20842e-11	0.288	6.97961e-11

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.130 GHz-days
Estimated T-Level:	1.700

Digits	B1	Curves	Complete	FacMiss
20	11000	34 / 100	0.340	71.055%
25	50000	34 / 280	0.121	88.546%

New Calculation Method

Total ECM effort:	3.130 GHz-days
Estimated T-Level:	1.700

Digits	B1	Complete	FacMiss
20	11000	1.143	31.870%
25	50000	0.104	90.090%
30	250000	0.006	99.357%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		10	0.846
50000	5000000	72008588682677195212759	3	0.254
50000	6750000		21	2.029

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-26T20:49:53	Oliver Kruse	ECM-HTC	50000	5000000						3	0.254
2019-05-18T11:13:05	MarkS	laptop64	50000	5000000	72008588682677195212759	75.931	3	2		3	0.254
2021-04-26T18:52:39	nordi	sweet16	50000	6750000						7	0.676
2021-08-12T00:26:44	Dylan Delgado	colab	50000	6750000						7	0.676
2021-11-16T10:25:07	Dylan Delgado	colab	50000	6750000						7	0.676
2022-04-21T11:29:11	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.593

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T22:01:40

Oliver Kruse

GTX-3

3655609817

4199120087

8FFB3CF5F470D1__

2017-11-13T21:19:23

Chang Chia-Tche

exbpc13

3655609817

4199120087

8FFB3CF5F470D1__

2019-05-21T11:27:59

vnatin

VIR7-1261

3655609817

4199120087

72008588682677195212759

40EE1C161E61C136

2019-05-21T11:37:55

ATH

ec2-PRPCFDC

3655609817

4199120087

72008588682677195212759

40EE1C161E61C136

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

10¹⁶

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