M27776213 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	4.2982	63.7681%	285000	34496700	2.8844	6.2113%	7.1826	66.0186%	2.2505%
PrimeNet	2⁶⁶	0.5317	62.1212%	130000	4500000	0.4941	5.2871%	1.0258	64.1239%	2.0027%
GPU72	2⁷⁰	8.6027	64.2857%	200000	6000000	0.6926	3.9159%	9.2953	65.6842%	1.3985%
Difference	-1	-4.3045	-0.5176%	+85000	+28496700	+2.1918	+2.2954%	-2.1127	+0.3343%	+0.3343%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

4.2982

63.7681%

285000

34496700

2.8844

6.2113%

7.1826

66.0186%

2.2505%

PrimeNet

2⁶⁶

0.5317

62.1212%

130000

4500000

0.4941

5.2871%

1.0258

64.1239%

2.0027%

GPU72

2⁷⁰

8.6027

64.2857%

200000

6000000

0.6926

3.9159%

9.2953

65.6842%

1.3985%

Difference

-1

-4.3045

-0.5176%

+85000

+28496700

+2.1918

+2.2954%

-2.1127

+0.3343%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27776213	3361310639983	13	41.612	60507 3⁶ × 83	-	729	729	1.157e-8	0.0010	0.0020
27776213	4972775413391	13	42.177	89515 5 × 17903	2008-09-08	5	17903	2.902e-8	0.0013	0.0024
27776213	320148631038001	15	48.186	5763000 2³ × 3 × 5³ × 17 × 113	2008-10-01	125	125	1.893e-6	0.0002	0.0003
27776213	1077770519610813649	19	59.903	19400962248 2³ × 3² × 269457809	2015-12-22	9	269457809	0.0041	19.705	36.804

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27776213

3361310639983

41.612

60507
3⁶ × 83

729

1.157e-8

0.0010

0.0020

27776213

4972775413391

42.177

89515
5 × 17903

2008-09-08

17903

2.902e-8

0.0013

0.0024

27776213

320148631038001

48.186

5763000
2³ × 3 × 5³ × 17 × 113

2008-10-01

125

1.893e-6

0.0002

0.0003

27776213

1077770519610813649

59.903

19400962248
2³ × 3² × 269457809

2015-12-22

269457809

0.0041

19.705

36.804

exponent	prime factors	composite factor	digits	bits*
27776213	3361310639983 4972775413391	16715042907277029598212353	26	83.789
27776213	3361310639983 320148631038001	1076118999884024478902993983	28	89.798
27776213	4972775413391 320148631038001	1592027241056558156205271391	28	90.363
27776213	3361310639983 1077770519610813649	3622721515027834478607541527967	31	101.515
27776213	4972775413391 1077770519610813649	5359510741198296715839840173759	31	102.080
27776213	320148631038001 1077770519610813649	345046756426517000039195048475649	33	108.088
27776213	3361310639983 4972775413391 320148631038001	5351298104506189309133599262000410626353	40	131.975
27776213	3361310639983 4972775413391 1077770519610813649	18014980479493009418229140267786298212806097	44	143.692
27776213	3361310639983 320148631038001 1077770519610813649	1159809333668074175513375944475848448781273967	46	149.701
27776213	4972775413391 320148631038001 1077770519610813649	1715840026828096760784197320386375740372015759	46	150.266
27776213	3361310639983 4972775413391 320148631038001 1077770519610813649	57674713386859978125173795519408823327037657413880 51492097	58	191.878

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-05-19T22:33:38	masser	Manual testing	285000	34496700		-	skipped known factor: 3361310639983 skipped known factor: 4972775413391 skipped known factor: 320148631038001	-	-	2.884	-	-	6.211%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-10-01T01:55:00	markr	Manual testing	?	?	320148631038001	48.186	15	5.43502e-7	52.94	1.11913e-6
2008-09-08T23:36:00	Will Edgington	Manual testing	?	?	4972775413391	42.177	13	7.92151e-9	52.94	1.63113e-8
2015-12-22T13:20:18	TJAOI	Manual testing	2⁵⁹	2⁶⁰*	1077770519610813649	59.903	19	0.001	52.94	0.003
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	1077770519610813649	59.903	19	0.004	52.94	0.008
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	320148631038001	48.186	15	1.89349e-6	52.94	3.89891e-6
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	3361310639983	41.612	13	1.15672e-8	52.94	2.38182e-8
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	4972775413391	42.177	13	2.90151e-8	52.94	5.97453e-8
2022-08-10T19:28:59	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.269	-	-
2022-08-10T19:28:59	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	0.538	-	-
2022-08-10T19:28:59	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.076	-	-
2022-08-03T12:34:05	masser	Manual testing	2⁶⁷	2⁶⁹		-	-	3.228	-	-

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

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