M5212787 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	5.7002	65.6716%	2500000	240000000	3.5354	10.2193%	9.2356	69.1797%	3.5081%
PrimeNet	2⁶²	0.1179	62.9032%	22000	500000	0.0110	3.0040%	0.1289	64.0176%	1.1144%
GPU72	2⁶⁶	2.8331	65.1515%	30000	600000	0.0140	1.9880%	2.8471	65.8443%	0.6928%
Difference	+1	+2.8671	+0.5201%	+2470000	+239400000	+3.5214	+8.2312%	+6.3885	+3.3354%	+3.3354%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.7002

65.6716%

2500000

240000000

3.5354

10.2193%

9.2356

69.1797%

3.5081%

PrimeNet

2⁶²

0.1179

62.9032%

22000

500000

0.0110

3.0040%

0.1289

64.0176%

1.1144%

GPU72

2⁶⁶

2.8331

65.1515%

30000

600000

0.0140

1.9880%

2.8471

65.8443%

0.6928%

Difference

+2.8671

+0.5201%

+2470000

+239400000

+3.5214

+8.2312%

+6.3885

+3.3354%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5212787	3637117873511	13	41.726	348865 5 × 11 × 6343	-	11	6343	8.497e-8	8.151e-5	0.0001
5212787	46794060612104999	17	55.377	4488391777 227 × 2017 × 9803	2015-01-21	2017	9803	0.0013	0.0006	0.0009
5212787	7712727500738627793721	22	72.708	739789243329780 2² × 3² × 5 × 7 × 4177 × 4889 × 28751	2021-09-27	4889	28751	233.50	0.0014	0.0023

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5212787

3637117873511

41.726

348865
5 × 11 × 6343

6343

8.497e-8

8.151e-5

0.0001

5212787

46794060612104999

55.377

4488391777
227 × 2017 × 9803

2015-01-21

2017

9803

0.0013

0.0006

0.0009

5212787

7712727500738627793721

72.708

739789243329780
2² × 3² × 5 × 7 × 4177 × 4889 × 28751

2021-09-27

4889

28751

233.50

0.0014

0.0023

exponent	prime factors	composite factor	digits	bits*
5212787	3637117873511 46794060612104999	170195514226444176988332781489	30	97.103
5212787	3637117873511 7712727500738627793721	28052099046456287602914645078024431	35	114.434
5212787	46794060612104999 7712727500738627793721	360909838154212452423938362196964911279	39	128.085
5212787	3637117873511 46794060612104999 7712727500738627793721	13126716230766483682470709533855611282493592592305 69	52	169.811

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-09-27T12:03:44	happy5214	Manual testing	2500000	2500000			7712727500738627793721	22	72.708	0.572	1.646	1.145	4.118%
2021-10-23T08:27:54	happy5214	Manual testing	2500000	240000000		-	skipped known factor: 3637117873511 skipped known factor: 46794060612104999 skipped known factor: 7712727500738627793721	-	-	3.535	-	-	10.219%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-09-27T12:03:44	happy5214	Manual testing	1250000	1250000	2	7	7712727500738627793721	P-1	22	72.708	0.435
2021-10-23T08:27:54	happy5214	Manual testing	1250000	85000000	2	7			-	-	1.459

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-01-21T12:40:00	TJAOI	Manual testing	2⁵⁵	2⁵⁶*	46794060612104999	55.377	17	0.000	1.787	0.001

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-23T08:51:08

kkmrkkblmbrbk

c4.xlarge

3637117873511

46794060612104999

8729ED7A116886__

2018-05-27T09:48:11

Battlemaxx

Work

3637117873511

46794060612104999

8729ED7A116886__

2021-09-27T12:51:27

happy5214

Manual testing

3637117873511

46794060612104999

7712727500738627793721

8729ED7A1168867F

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 = 2500000, B2 = 240000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 1250000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁵⁶

2⁴⁰

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