M386 747 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
Actual	2⁶⁷	76.8304	71.6418%	50000	50000	0.0007	0.4206%	76.8311	71.7611%
Target	2⁴⁴	0.0000	56.8182%	7000	1000000	0.0009	12.7895%	0.0009	62.3409%
Difference	+23	+76.8304	+14.8236%	+43000	-950000	-0.0002	-12.3689%	+76.8302	+9.4202%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁶⁷

76.8304

71.6418%

50000

0.0007

0.4206%

76.8311

71.7611%

Target

2⁴⁴

0.0000

56.8182%

7000

1000000

0.0009

12.7895%

0.0009

62.3409%

Difference

+23

+76.8304

+14.8236%

+43000

-950000

-0.0002

-12.3689%

+76.8302

+9.4202%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
386747	5373006488906856431	19	62.220	6946410041845 5 × 229 × 18047 × 336163	-	18047	336163	1.8660	0.0005	0.0005
386747	141588541435123636324439	24	76.906	183050600825764177 11 × 16640963711433107	2014-10-31	11	16640963711433107	72,265	12,744,667	23,803,489

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

386747

5373006488906856431

62.220

6946410041845
5 × 229 × 18047 × 336163

18047

336163

1.8660

0.0005

386747

141588541435123636324439

76.906

183050600825764177
11 × 16640963711433107

2014-10-31

16640963711433107

72,265

12,744,667

23,803,489

exponent	prime factors	composite factor	digits	bits*
386747	5373006488906856431 141588541435123636324439	760756151885776608409715058841154709617209	42	139.126

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-02-06	Lisander Viaene	Manual testing	50000	50000		-		-	-	0.001	-	-	0.421%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-12-01	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-

ECM factoring results:

Total ECM effort:	10.137 GHz-days
Estimated T-Level:	26.394

Digits	B1	Complete	FacMiss
20	11000	22.476	0.000%
25	50000	2.896	5.522%
30	250000	0.279	75.675%
35	1000000	0.022	97.870%
40	3000000	0.001	99.862%

ECM Summary

B1	B2	factor	curves	GHz-days
		141588541435123636324439	1	0.00000e+0
50000	5000000		244	2.566
250000	25000000		144	7.571

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-10-31	TJAOI	Manual testing	50000	5000000						13	0.137
2014-10-31	TJAOI	Manual testing			141588541435123636324439	76.906		1		1	-
2015-04-10	TJAOI	Manual testing	50000	5000000						50	0.526
2016-01-04	TJAOI	Manual testing	50000	5000000						90	0.946
2016-05-27	TJAOI	Manual testing	50000	5000000						91	0.957
2018-02-23	TJAOI	Manual testing	250000	25000000						44	2.313
2020-11-27	TJAOI	Manual testing	250000	25000000						100	5.258

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-23

Oliver Kruse

Ollaptop

04E67766D9BFC3__

2017-09-23

Oliver Kruse

Manual testing

04E67766D9BFC3__

2017-10-13

Oliver Kruse

Threadripper

04E67766D9BFC3__

2017-12-15

ATH

xps

5373006488906856431

141588541435123636324439

04E67766D9BFC3__

2020-04-18

Oliver Kruse

AddPrpType5

5373006488906856431

141588541435123636324439

1748BD9D126A3A__

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 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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