M1600061 Mersenne number exponent details

Residue

Status

L-L

C31FD444A0F485E3

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	2⁷⁰	149.3385	70.0000%	2000000	40000000	0.2636	5.2461%	149.6021	71.5738%	1.5738%
PrimeNet	2⁵⁷	0.0120	63.1579%	7000	120000	0.0009	2.5481%	0.0129	64.0967%	0.9388%
GPU72	2⁶¹	0.1920	65.5738%	6500	60000	0.0006	1.0563%	0.1926	65.9374%	0.3637%
Difference	+9	+149.1465	+4.4262%	+1993500	+39940000	+0.2630	+4.1897%	+149.4095	+5.6364%	+5.6364%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

149.3385

70.0000%

2000000

40000000

0.2636

5.2461%

149.6021

71.5738%

1.5738%

PrimeNet

2⁵⁷

0.0120

63.1579%

7000

120000

0.0009

2.5481%

0.0129

64.0967%

0.9388%

GPU72

2⁶¹

0.1920

65.5738%

6500

60000

0.0006

1.0563%

0.1926

65.9374%

0.3637%

Difference

+149.1465

+4.4262%

+1993500

+39940000

+0.2630

+4.1897%

+149.4095

+5.6364%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1600061	3573352964183027918221155860497	31	101.495	1116630229779685873920168 2³ × 3³ × 139 × 283 × 4663 × 488333 × 57712901	2014-05-21	488333	57712901	1.187e+11	0.2336	0.3804

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1600061

3573352964183027918221155860497

101.495

1116630229779685873920168
2³ × 3³ × 139 × 283 × 4663 × 488333 × 57712901

2014-05-21

488333

57712901

1.187e+11

0.2336

0.3804

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-10-31T01:34:00	BigBrother	BigBrother	2000000	40000000		-		-	-	0.264	-	-	5.246%
2014-05-21T22:41:00	mikr	Colorovo	2000000	40000000			3573352964183027918221155860497	31	101.495	0.264	0.143	0.527	5.246%
2016-03-17T19:17:11	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	3.711%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2010-05-01T21:20:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.096	-	-
2010-06-23T00:16:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.997	-	-
2011-11-09T20:49:00	Never Odd Or Even	Manual testing	2⁶³	2⁶⁴		-	-	1.227	-	-
2011-11-09T20:49:00	Never Odd Or Even	Manual testing	2⁶⁴	2⁶⁵		-	-	2.335	-	-
2012-03-13T11:11:00	Never Odd Or Even	Manual testing	2⁶⁵	2⁶⁶		-	-	4.670	-	-
2014-01-18T11:18:00	Never Odd Or Even	Manual testing	2⁶⁶	2⁶⁷		-	-	9.341	-	-
2014-01-18T11:18:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	18.68	-	-
2014-01-18T11:18:00	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	37.36	-	-
2014-01-18T11:18:00	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰		-	-	74.72	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.811 GHz-days
Estimated T-Level:	3.300

Digits	B1	Curves	Complete	FacMiss
20	11000	66 / 100	0.660	51.514%
25	50000	66 / 280	0.236	78.967%
30	250000	54 / 640	0.084	91.903%

New Calculation Method

Total ECM effort:	15.811 GHz-days
Estimated T-Level:	3.300

Digits	B1	Complete	FacMiss
20	11000	4.887	0.754%
25	50000	0.686	50.379%
30	250000	0.072	93.018%
35	1000000	0.006	99.408%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	0.673
250000	25000000		54	15.14

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-03-27T09:38:00	Sturle Sunde	lara	50000	5000000						3	0.168
2009-05-17T12:04:00	S36049	Wolle3	50000	5000000						3	0.168
2010-03-28T22:42:00	James Hintz	ryan	50000	5000000						3	0.168
2011-10-19T23:37:00	S36049	Wolle5	50000	5000000						3	0.168
2011-12-20T18:47:00	Never Odd Or Even	Sandy	250000	25000000						54	15.14

date	userid	compid	res64	spent (GHz-days)
1998-11-07T00:00:00	ANONYMOUS	v4_computers	C31FD444A0F485E3	0.071

date

userid

compid

res64

spent (GHz-days)

1998-11-07T00:00:00

ANONYMOUS

v4_computers

C31FD444A0F485E3

0.071

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T03:25:48

Oliver Kruse

GTX-1

3573352964183027918221155860497

E369A99B4E7F28__

2017-10-31T23:58:31

kkmrkkblmbrbk

c4.xlarge

3573352964183027918221155860497

E369A99B4E7F28__

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 = 2000000, B2 = 40000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

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

B1 = 500000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

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