M6056221 Mersenne number exponent details

Residue

Status

L-L

3F18750080F29469

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	4.9063	65.6716%	30000	360000	0.0123	1.5467%	4.9187	66.2026%	0.5310%
PrimeNet	2⁶²	0.1014	62.9032%	26000	600000	0.0147	3.3348%	0.1162	64.1403%	1.2371%
GPU72	2⁶⁶	2.4386	65.1515%	40000	900000	0.0223	2.4209%	2.4609	65.9952%	0.8436%
Difference	+1	+2.4678	+0.5201%	-10000	-540000	-0.0100	-0.8741%	+2.4578	+0.2075%	+0.2075%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.9063

65.6716%

30000

360000

0.0123

1.5467%

4.9187

66.2026%

0.5310%

PrimeNet

2⁶²

0.1014

62.9032%

26000

600000

0.0147

3.3348%

0.1162

64.1403%

1.2371%

GPU72

2⁶⁶

2.4386

65.1515%

40000

900000

0.0223

2.4209%

2.4609

65.9952%

0.8436%

Difference

+2.4678

+0.5201%

-10000

-540000

-0.0100

-0.8741%

+2.4578

+0.2075%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6056221	64855005652864025359	20	65.814	5354412070899 3 × 31 × 601 × 95797543	2011-07-31	601	95797543	2.0804	1.3414	2.5050

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6056221

64855005652864025359

65.814

5354412070899
3 × 31 × 601 × 95797543

2011-07-31

601

95797543

2.0804

1.3414

2.5050

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-11-15T00:00:00	ANONYMOUS	v4_computers	30000	360000		-		-	-	0.012	-	-	1.547%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.101	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		64855005652864025359	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-07-31T02:10:00	JimBa	T61-3			64855005652864025359	65.814		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	netconx	v4_computers	3F18750080F29469	1.073
2001-06-03T00:00:00	ANONYMOUS	v4_computers	3F18750080F29469	1.073

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:42:39

kkmrkkblmbrbk

Manual testing

64855005652864025359

D3017D44A82515__

2018-09-16T14:10:35

ANONYMOUS

64855005652864025359

D3017D44A82515__

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 = 30000, B2 = 360000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶²

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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