M42 654 757 Mersenne number exponent details

Residue

Status

L-L

FBB049CC93BBE2B1

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁴	89.6938	64.8649 %	2000000	60000000	11.0282	5.6775 %	100.7219	66.8597 %
Target	2⁷²	22.4203	63.8889 %	300000	45000000	5.8462	3.8762 %	28.2665	65.2886 %
Difference	+2	+67.2734	+0.9760 %	+1700000	+15000000	+5.1820	+1.8013%	+72.4554	+1.5710 %

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷⁴

89.6938

64.8649 %

2000000

60000000

11.0282

5.6775 %

100.7219

66.8597 %

Target

2⁷²

22.4203

63.8889 %

300000

45000000

5.8462

3.8762 %

28.2665

65.2886 %

Difference

+67.2734

+0.9760 %

+1700000

+15000000

+5.1820

+1.8013%

+72.4554

+1.5710 %

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
42654757	236486695851916701794399	24	77.646	2772102251712707 149 × 1104157 × 16849699	2021-02-11	1104157	16849699	967.18	4.1933	4.8027
42654757	1056984475594071874805555854159	31	99.738	12389995277596727075547 3⁸ × 167 × 9907 × 423803 × 2693261	2021-02-11	423803	2693261	3.722e+9	1.1700	1.8434

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

42654757

236486695851916701794399

77.646

2772102251712707
149 × 1104157 × 16849699

2021-02-11

1104157

16849699

967.18

4.1933

4.8027

42654757

1056984475594071874805555854159

99.738

12389995277596727075547
3⁸ × 167 × 9907 × 423803 × 2693261

2021-02-11

423803

2693261

3.722e+9

1.1700

1.8434

exponent	prime factors	composite factor	digits	bits*
42654757	236486695851916701794399 1056984475594071874805555854159	24996276620001294756120380875665317752503117444705 5441	54	177.384

P-1 results:

date	user	comp	B1	B2	BS	stage	factor	digits	bits*	GHz-days	Fac Prob
2008-06-22	ANONYMOUS	v4_computers	415000	2178750				-	-	1.092	2.912%
2021-02-11	ViliamF	Manual testing	2000000	60000000		2	236486695851916701794399 1056984475594071874805555854159	54	177.384	11.42	6.734%

Trial Factoring results:

			Bits		Factor
date	userid	compid	from	to	factor	bits*	digits	GHz-days
2007-07-04	ComputerraRU	v4_computers	2⁶²	2⁶⁶				0.332
2007-09-13	David Hruska	v4_computers	2¹	2⁶⁸				0.701
2014-02-17	Grant McCracken	Manual testing	2⁶⁸	2⁶⁹				1.402
2014-05-01	Grant McCracken	Manual testing	2⁶⁹	2⁷⁰				2.803
2015-04-05	Mark Rose	Manual testing	2⁷⁰	2⁷¹				5.606
2015-08-31	ANONYMOUS	Manual testing	2⁷¹	2⁷²				11.21
2019-10-04	ANONYMOUS	Manual testing	2⁷²	2⁷³				22.42
2020-01-11	ANONYMOUS	Manual testing	2⁷³	2⁷⁴				44.85

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2008-07-25	ANONYMOUS	v4_computers	FBB049CC93BBE2B1	62.87
2017-04-08	ANONYMOUS		FBB049CC93BBE2B1	65.11

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 = 415000, B2 = 2178750 (P-1 stage 2)

B1 = 415000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁶

this exponent TF target: 72

TF double-checked to: 67

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