M2430569 Mersenne number exponent details

Residue

Status

L-L

1502EFCC34FADD72

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	12.2251	67.1642%	2000000	60000000	0.5055	7.6252%	12.7305	69.6680%	2.5038%
PrimeNet	2⁵⁹	0.0316	62.7119%	10000	180000	0.0019	2.5245%	0.0335	63.6532%	0.9413%
GPU72	2⁶³	0.6566	65.0794%	10000	150000	0.0017	1.3055%	0.6584	65.5352%	0.4559%
Difference	+4	+11.5684	+2.0848%	+1990000	+59850000	+0.5037	+6.3197%	+12.0722	+4.1327%	+4.1327%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.2251

67.1642%

2000000

60000000

0.5055

7.6252%

12.7305

69.6680%

2.5038%

PrimeNet

2⁵⁹

0.0316

62.7119%

10000

180000

0.0019

2.5245%

0.0335

63.6532%

0.9413%

GPU72

2⁶³

0.6566

65.0794%

10000

150000

0.0017

1.3055%

0.6584

65.5352%

0.4559%

Difference

+11.5684

+2.0848%

+1990000

+59850000

+0.5037

+6.3197%

+12.0722

+4.1327%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2430569	441996019974799459625207	24	78.548	90924392595889987 23 × 503 × 7859313043123	2016-06-10	503	7859313043123	46,485	41,944	78,340

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2430569

441996019974799459625207

78.548

90924392595889987
23 × 503 × 7859313043123

2016-06-10

503

7859313043123

46,485

41,944

78,340

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.289%
2010-10-09T08:01:00	Oscar Östlin		40000	640000		-		-	-	0.007	-	-	1.664%
2011-01-18T00:07:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.614%
2011-01-28T20:02:00	James Heinrich	i7-920	165000	3795000		-		-	-	0.036	-	-	3.421%
2018-09-28T17:00:18	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.505	-	-	7.625%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-11T00:42:00	Sturle Sunde	gerle.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-05T13:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.126	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.404	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.808	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.537	-	-
2015-10-25T20:34:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.074	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.784 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	1.784 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.645	52.458%
25	50000	0.058	94.336%
30	250000	0.004	99.642%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.605
50000	5000000	441996019974799459625207	2	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-07T23:03:00	Anu Järvi	Anu	50000	5000000						3	0.268
2010-03-04T07:45:00	SubPrime	abd0	50000	5000000						3	0.268
2012-03-25T13:36:00	S36049	Wolle5	50000	5000000						3	0.268
2013-12-16T14:16:00	arnaud	srv-630	50000	5000000						3	0.268
2015-07-04T06:19:00	guru	w1	50000	5000000						3	0.268
2016-02-20T21:32:07	Bruce	Desk8	50000	5000000						3	0.268
2016-06-10T15:47:19	Bruce	Desk6	50000	5000000	441996019974799459625207	78.548	2	2		2	0.178

date	userid	compid	res64	spent (GHz-days)
1999-09-07T00:00:00	ANONYMOUS	v4_computers	1502EFCC34FADD72	0.164

date

userid

compid

res64

spent (GHz-days)

1999-09-07T00:00:00

ANONYMOUS

v4_computers

1502EFCC34FADD72

0.164

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-13T05:55:20

Oliver Kruse

GTX-3

48C752B898DC36__

2017-11-27T15:34:24

kkmrkkblmbrbk

c4.xlarge

441996019974799459625207

48C752B898DC36__

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 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 165000, B2 = 3795000 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

B1 = 40000, B2 = 640000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 40000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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