M27830791 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	2⁶⁹	4.2897	63.7681%	285000	34496700	2.8844	6.2127%	7.1742	66.0191%	2.2510%
PrimeNet	2⁶⁶	0.5307	62.1212%	130000	4500000	0.4941	5.2885%	1.0247	64.1244%	2.0032%
GPU72	2⁷⁰	8.5858	64.2857%	200000	6000000	0.6926	3.9169%	9.2784	65.6846%	1.3989%
Difference	-1	-4.2961	-0.5176%	+85000	+28496700	+2.1918	+2.2958%	-2.1043	+0.3345%	+0.3345%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

4.2897

63.7681%

285000

34496700

2.8844

6.2127%

7.1742

66.0191%

2.2510%

PrimeNet

2⁶⁶

0.5307

62.1212%

130000

4500000

0.4941

5.2885%

1.0247

64.1244%

2.0032%

GPU72

2⁷⁰

8.5858

64.2857%

200000

6000000

0.6926

3.9169%

9.2784

65.6846%

1.3989%

Difference

-1

-4.2961

-0.5176%

+85000

+28496700

+2.1918

+2.2958%

-2.1043

+0.3345%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27830791	3840649159	10	31.839	69 3 × 23	-	3	23	1.043e-11	5.489e-6	8.195e-6
27830791	69081190938934463	17	55.939	1241092841 1241092841	2015-08-06	1	1241092841	0.0003	90.761	169.52
27830791	2254783633538627881	19	60.968	40508795340 2² × 3² × 5 × 13 × 19 × 911129	2016-03-18	19	911129	0.0084	0.0667	0.1244
27830791	5105118352609600943	19	62.147	91717090481 191 × 480194191	2016-07-04	191	480194191	0.0251	35.117	65.588

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27830791

3840649159

31.839

69
3 × 23

1.043e-11

5.489e-6

8.195e-6

27830791

69081190938934463

55.939

1241092841
1241092841

2015-08-06

1241092841

0.0003

90.761

169.52

27830791

2254783633538627881

60.968

40508795340
2² × 3² × 5 × 13 × 19 × 911129

2016-03-18

911129

0.0084

0.0667

0.1244

27830791

5105118352609600943

62.147

91717090481
191 × 480194191

2016-07-04

191

480194191

0.0251

35.117

65.588

exponent	prime factors	composite factor	digits	bits*
27830791	3840649159 69081190938934463	265316617882337065677066617	27	87.778
27830791	3840649159 2254783633538627881	8659832865877095365176602079	28	92.806
27830791	3840649159 5105118352609600943	19606968507545529317058556937	29	93.985
27830791	69081190938934463 2254783633538627881	155763138714466385124438749203562903	36	116.907
27830791	69081190938934463 5105118352609600943	352667655682482397526502480059998609	36	118.086
27830791	2254783633538627881 5105118352609600943	11510937308741810125458086095183691783	38	123.114
27830791	3840649159 69081190938934463 2254783633538627881	598231567706915663161945792475675783210548577	45	148.746
27830791	3840649159 69081190938934463 5105118352609600943	1354472735203427591092465430253847927197019831	46	149.924
27830791	3840649159 2254783633538627881 5105118352609600943	44209471694120956406478282851216839796894160497	47	154.953
27830791	69081190938934463 2254783633538627881 5105118352609600943	79518925811129738683085057837269339375192830062861 7529	54	179.053
27830791	3840649159 69081190938934463 2254783633538627881 5105118352609600943	30540429554109882371308039490817484712781992824375 99084086508111	64	210.892

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-05-21T03:33:30	masser	Manual testing	285000	34496700		-	skipped known factor: 3840649159 skipped known factor: 2254783633538627881	-	-	2.884	-	-	6.213%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-05-21T03:33:30

masser

Manual testing

285000

34496700

skipped known factor: 3840649159
skipped known factor: 2254783633538627881

2.884

-

-

6.213%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-02-24T12:19:00	TJAOI	Manual testing	2⁵⁵	2⁵⁶*	69081190938934463	55.939	17	0.000	53.04	0.000
2022-06-25T07:44:49	LordJulius	Manual testing	2¹	2⁶⁰	3840649159	31.839	10	1.04329e-11	53.04	2.14809e-11
2022-06-25T07:44:49	LordJulius	Manual testing	2¹	2⁶⁰	69081190938934463	55.939	17	0.000	53.04	0.001
2016-03-18T12:45:50	TJAOI	Manual testing	2⁶⁰	2⁶¹*	2254783633538627881	60.968	19	0.003	53.03	0.006
2022-06-25T07:44:49	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.011	-	-
2016-07-04T16:30:10	TJAOI	Manual testing	2⁶²	2⁶³*	5105118352609600943	62.147	19	0.003	52.99	0.006
2022-08-10T19:29:02	LordJulius	Manual testing	2¹	2⁶⁵	2254783633538627881	60.968	19	0.008	53.03	0.017
2022-08-10T19:29:02	LordJulius	Manual testing	2¹	2⁶⁵	3840649159	31.839	10	1.04329e-11	53.04	2.14809e-11
2022-08-10T19:29:02	LordJulius	Manual testing	2¹	2⁶⁵	5105118352609600943	62.147	19	0.025	52.99	0.052
2022-08-10T19:29:02	LordJulius	Manual testing	2¹	2⁶⁵	69081190938934463	55.939	17	0.000	53.04	0.001
2022-08-10T19:29:02	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.269	-	-
2022-08-10T19:29:02	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	0.537	-	-
2022-08-10T19:29:02	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.074	-	-
2022-08-05T12:41:58	masser	Manual testing	2⁶⁷	2⁶⁹		-	-	3.222	-	-

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 = 285000, B2 = 34496700 (P-1 stage 2)

B1 = 285000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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