M1652909 Mersenne number exponent details

Residue

Status

L-L

B8F456D87ED0EAAA

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	17.9767	68.6567%	500000	15000000	0.0880	5.0068%	18.0648	70.2260%	1.5693%
PrimeNet	2⁵⁷	0.0116	63.1579%	7000	120000	0.0009	2.5643%	0.0125	64.1026%	0.9448%
GPU72	2⁶¹	0.1858	65.5738%	7000	70000	0.0007	1.1515%	0.1866	65.9702%	0.3964%
Difference	+6	+17.7909	+3.0829%	+493000	+14930000	+0.0873	+3.8552%	+17.8782	+4.2558%	+4.2558%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.9767

68.6567%

500000

15000000

0.0880

5.0068%

18.0648

70.2260%

1.5693%

PrimeNet

2⁵⁷

0.0116

63.1579%

7000

120000

0.0009

2.5643%

0.0125

64.1026%

0.9448%

GPU72

2⁶¹

0.1858

65.5738%

7000

70000

0.0007

1.1515%

0.1866

65.9702%

0.3964%

Difference

+17.7909

+3.0829%

+493000

+14930000

+0.0873

+3.8552%

+17.8782

+4.2558%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1652909	12864471208340125471	20	63.480	3891463839915 3 × 5 × 83 × 3125673767	2010-05-14	83	3125673767	1.5093	11.621	21.705

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1652909

12864471208340125471

63.480

3891463839915
3 × 5 × 83 × 3125673767

2010-05-14

3125673767

1.5093

11.621

21.705

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:17:55	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.007%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.006	-	-
1997-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.006	-	-
1998-02-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.006	-	-
1998-11-07T00:00:00	Jo Yeong Uk	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-05-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2022-03-08T20:45:51	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.070	-	-
2022-03-09T02:40:38	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.093	-	-
2010-04-28T22:20:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.093	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.698 GHz-days
Estimated T-Level:	24.429

Digits	B1	Curves	Complete	FacMiss
20	11000	248 / 100	2.480	8.270%
25	50000	248 / 280	0.886	41.177%

New Calculation Method

Total ECM effort:	14.698 GHz-days
Estimated T-Level:	24.429

Digits	B1	Complete	FacMiss
20	11000	9.538	0.007%
25	50000	0.883	41.372%
30	250000	0.056	94.585%
35	1000000	0.003	99.740%

ECM Summary

B1	B2	factor	curves	GHz-days
		12864471208340125471	1	0.00000e+0
50000	5000000		248	14.70

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-20T00:25:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-06-08T01:51:00	Lupo	yorick	50000	5000000						3	0.178
2010-05-14T10:17:00	SubPrime	abd0			12864471208340125471	63.480		1		1	-
2015-02-08T21:27:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2019-12-09T17:15:28	TJAOI	Manual testing	50000	5000000						241	14.28

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-04T00:00:00	ANONYMOUS	v4_computers	B8F456D87ED0EAAA	0.078
1997-12-21T00:00:00	ANONYMOUS	v4_computers	B8F456D87ED0EAAA	0.078
1998-02-01T00:00:00	ANONYMOUS	v4_computers	B8F456D87ED0EAAA	0.078
1999-01-02T00:00:00	Jo Yeong Uk	v4_computers	B8F456D87ED0EAAA	0.078

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T19:10:54

Oliver Kruse

GTX-2

12864471208340125471

471176AD24F6E7__

2017-11-02T08:58:50

kkmrkkblmbrbk

c4.xlarge

12864471208340125471

471176AD24F6E7__

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

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