M27779551 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	4.2977	63.7681%	285000	34496700	2.8844	6.2114%	7.1821	66.0186%	2.2505%
PrimeNet	2⁶⁶	0.5316	62.1212%	130000	4500000	0.4941	5.2872%	1.0257	64.1239%	2.0027%
GPU72	2⁷⁰	8.6017	64.2857%	200000	6000000	0.6926	3.9159%	9.2943	65.6843%	1.3986%
Difference	-1	-4.3040	-0.5176%	+85000	+28496700	+2.1918	+2.2954%	-2.1122	+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

4.2977

63.7681%

285000

34496700

2.8844

6.2114%

7.1821

66.0186%

2.2505%

PrimeNet

2⁶⁶

0.5316

62.1212%

130000

4500000

0.4941

5.2872%

1.0257

64.1239%

2.0027%

GPU72

2⁷⁰

8.6017

64.2857%

200000

6000000

0.6926

3.9159%

9.2943

65.6843%

1.3986%

Difference

-1

-4.3040

-0.5176%

+85000

+28496700

+2.1918

+2.2954%

-2.1122

+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
27779551	34074619493009	14	44.954	613304 2³ × 31 × 2473	-	31	2473	1.476e-7	0.0002	0.0003
27779551	44179486728361	14	45.328	795180 2² × 3 × 5 × 29 × 457	2008-09-08	29	457	1.884e-7	7.023e-5	7.922e-5
27779551	910381166549216287	18	59.659	16385814993 3 × 137 × 223 × 178781	2015-12-04	223	178781	0.0033	0.0134	0.0244
27779551	20619417928310054143	20	64.161	371125831521 3 × 433 × 977 × 292427	2017-08-01	977	292427	0.2038	0.0226	0.0399

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27779551

34074619493009

44.954

613304
2³ × 31 × 2473

2473

1.476e-7

0.0002

0.0003

27779551

44179486728361

45.328

795180
2² × 3 × 5 × 29 × 457

2008-09-08

457

1.884e-7

7.023e-5

7.922e-5

27779551

910381166549216287

59.659

16385814993
3 × 137 × 223 × 178781

2015-12-04

223

178781

0.0033

0.0134

0.0244

27779551

20619417928310054143

64.161

371125831521
3 × 433 × 977 × 292427

2017-08-01

977

292427

0.2038

0.0226

0.0399

exponent	prime factors	composite factor	digits	bits*
27779551	34074619493009 44179486728361	1505399199665342141921528249	28	90.282
27779551	34074619493009 910381166549216287	31020891843766198267382225437583	32	104.613
27779551	44179486728361 910381166549216287	40220172665310906111442206015607	32	104.988
27779551	34074619493009 20619417928310054143	702598820074493022210307999986287	33	109.114
27779551	44179486728361 20619417928310054143	910955300710302902351749843649623	33	109.489
27779551	910381166549216287 20619417928310054143	18771529747140731654915150859187427041	38	123.820
27779551	34074619493009 44179486728361 910381166549216287	1370487079513590747844429221597327124281391463	46	149.941
27779551	34074619493009 44179486728361 20619417928310054143	31040455246843162620115803491204311886493985607	47	154.443
27779551	34074619493009 910381166549216287 20619417928310054143	63963273343551987963057821531239783594950659705636 9	51	168.774
27779551	44179486728361 910381166549216287 20619417928310054143	82931654933483767233525118747701309928249447300980 1	51	169.148
27779551	34074619493009 44179486728361 910381166549216287 20619417928310054143	28258645857839819782689510482906645302914923601578 069984907981209	65	214.102

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-05-21T03:34:44	masser	Manual testing	285000	34496700		-	skipped known factor: 34074619493009 skipped known factor: 44179486728361 skipped known factor: 910381166549216287 skipped known factor: 20619417928310054143	-	-	2.884	-	-	6.211%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T23:36:00	Will Edgington	Manual testing	?	?	44179486728361	45.328	14	1.97215e-8	52.95	4.06085e-8
2015-12-04T13:44:35	TJAOI	Manual testing	2⁵⁹	2⁶⁰*	910381166549216287	59.659	18	0.001	52.94	0.001
2022-06-25T07:44:46	LordJulius	Manual testing	2⁶⁰	2⁶⁴		-	-	0.123	-	-
2017-08-01T11:25:57	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	20619417928310054143	64.161	20	0.076	52.69	0.155
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	20619417928310054143	64.161	20	0.204	52.69	0.418
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	34074619493009	44.954	14	1.47619e-7	52.95	3.03962e-7
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	44179486728361	45.328	14	1.88450e-7	52.95	3.88037e-7
2022-08-10T19:28:59	LordJulius	Manual testing	2¹	2⁶⁵	910381166549216287	59.659	18	0.003	52.94	0.007
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

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