M27760451 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	4.3006	63.7681%	285000	34496700	2.8844	6.2109%	7.1850	66.0184%	2.2503%
PrimeNet	2⁶⁶	0.5320	62.1212%	130000	4500000	0.4941	5.2867%	1.0261	64.1238%	2.0026%
GPU72	2⁷⁰	8.6076	64.2857%	200000	6000000	0.6926	3.9156%	9.3002	65.6841%	1.3984%
Difference	-1	-4.3070	-0.5176%	+85000	+28496700	+2.1918	+2.2953%	-2.1151	+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

4.3006

63.7681%

285000

34496700

2.8844

6.2109%

7.1850

66.0184%

2.2503%

PrimeNet

2⁶⁶

0.5320

62.1212%

130000

4500000

0.4941

5.2867%

1.0261

64.1238%

2.0026%

GPU72

2⁷⁰

8.6076

64.2857%

200000

6000000

0.6926

3.9156%

9.3002

65.6841%

1.3984%

Difference

-1

-4.3070

-0.5176%

+85000

+28496700

+2.1918

+2.2953%

-2.1151

+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
27760451	55520903	8	25.727	1 1	-	1	1	1.611e-13	1.342e-6	2.732e-6
27760451	2269916557369	13	41.046	40884 2² × 3 × 3407	2008-09-08	4	3407	1.952e-8	0.0003	0.0005
27760451	795862148882921	15	49.500	14334460 2² × 5 × 7² × 14627	2014-04-30	49	14627	4.584e-6	0.0011	0.0020
27760451	1273460884488819097	19	60.143	22936602948 2² × 3 × 7 × 139 × 233 × 8431	2016-01-15	233	8431	0.0093	0.0009	0.0012
27760451	699394651502477005777621057	27	89.176	12596961257986712928 2⁵ × 3 × 23² × 1553 × 47659 × 3351371	2022-05-19	47659	3351371	8,668,759	0.3056	0.4578

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27760451

55520903

25.727

1
1

1.611e-13

1.342e-6

2.732e-6

27760451

2269916557369

41.046

40884
2² × 3 × 3407

2008-09-08

3407

1.952e-8

0.0003

0.0005

27760451

795862148882921

49.500

14334460
2² × 5 × 7² × 14627

2014-04-30

14627

4.584e-6

0.0011

0.0020

27760451

1273460884488819097

60.143

22936602948
2² × 3 × 7 × 139 × 233 × 8431

2016-01-15

233

8431

0.0093

0.0009

0.0012

27760451

699394651502477005777621057

89.176

12596961257986712928
2⁵ × 3 × 23² × 1553 × 47659 × 3351371

2022-05-19

47659

3351371

8,668,759

0.3056

0.4578

exponent	prime factors	composite factor	digits	bits*
27760451	55520903 2269916557369	126027816999778184207	21	66.772
27760451	55520903 795862148882921	44186985169500215197663	23	75.226
27760451	55520903 1273460884488819097	70703698241997929669084591	26	85.870
27760451	2269916557369 795862148882921	1806540669132614565360794849	28	90.545
27760451	2269916557369 1273460884488819097	2890649946862942016034463275793	31	101.189
27760451	795862148882921 1273460884488819097	1013499316047616806115593001942337	34	109.643
27760451	55520903 699394651502477005777621057	38831022604787830097509738276454471	35	114.903
27760451	55520903 2269916557369 795862148882921	100300769256466987419783850814228647	36	116.272
27760451	55520903 2269916557369 1273460884488819097	160491495306732557966873880192365401079	39	126.916
27760451	2269916557369 699394651502477005777621057	1587567499580794108330820712488082919033	40	130.222
27760451	55520903 795862148882921 1273460884488819097	56270397216846076073513645848319304170311	41	135.369
27760451	795862148882921 699394651502477005777621057	556621730261983002238004405172233397267497	42	138.676
27760451	1273460884488819097 699394651502477005777621057	890651731509093757961312921891714895890925529	45	149.320
27760451	2269916557369 795862148882921 1273460884488819097	2300558878378642436214814012438897733290431353	46	150.689
27760451	55520903 2269916557369 699394651502477005777621057	88143181150177810351606988688441740403588046799	47	155.949
27760451	55520903 795862148882921 699394651502477005777621057	30904141093567722854905025493140268743049165989791	50	164.402
27760451	55520903 1273460884488819097 699394651502477005777621057	49449788391898438153675532488996479238415174875832 687	53	175.046
27760451	55520903 2269916557369 795862148882921 1273460884488819097	12772910633224940397276637594766083447693790997807 1759	54	176.415
27760451	2269916557369 795862148882921 699394651502477005777621057	12634848817130565828992859817652126506344041218395 35393	55	179.722
27760451	2269916557369 1273460884488819097 699394651502477005777621057	20217051122018610061885903635477758714843859209148 35173201	58	190.365
27760451	795862148882921 1273460884488819097 699394651502477005777621057	70883600094512175718022317278985680675690317281288 8150990209	60	198.819
27760451	55520903 2269916557369 795862148882921 699394651502477005777621057	70149821559557088372662715762846140350245639711453 026119819879	62	205.448
27760451	55520903 2269916557369 1273460884488819097 699394651502477005777621057	11224689342916364134407912528127080002642505672967 8234912280920503	66	216.092
27760451	55520903 795862148882921 1273460884488819097 699394651502477005777621057	39355214851382013403592724294817879151839765638136 600180976747838727	68	224.546
27760451	2269916557369 795862148882921 1273460884488819097 699394651502477005777621057	16089985750045600093530721412702701980761011477071 04347689747081705800121	73	239.865
27760451	55520903 2269916557369 795862148882921 1273460884488819097 699394651502477005777621057	89333053809966400836971011107468968451173998440034 812898960721817920803055429263	80	265.592

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-05-19T22:33:36	masser	Manual testing	285000	34496700			699394651502477005777621057	27	89.176	2.884	51.40	5.769	6.211%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-05-19T22:33:36

masser

Manual testing

285000

34496700

699394651502477005777621057

89.176

2.884

51.40

5.769

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	?	?	2269916557369	41.046	13	8.96301e-9	52.92	1.84562e-8
2014-04-30T11:38:00	TJAOI	Manual testing	?	?	795862148882921	49.500	15	1.88287e-6	52.92	3.87712e-6
2016-01-15T13:04:48	TJAOI	Manual testing	2⁶⁰	2⁶¹*	1273460884488819097	60.143	19	0.004	52.90	0.008
2022-08-10T19:28:58	LordJulius	Manual testing	2¹	2⁶⁵	1273460884488819097	60.143	19	0.009	52.90	0.019
2022-08-10T19:28:58	LordJulius	Manual testing	2¹	2⁶⁵	2269916557369	41.046	13	1.95158e-8	52.92	4.01860e-8
2022-08-10T19:28:58	LordJulius	Manual testing	2¹	2⁶⁵	55520903	25.727	8	1.61058e-13	52.92	3.31642e-13
2022-08-10T19:28:58	LordJulius	Manual testing	2¹	2⁶⁵	795862148882921	49.500	15	4.58438e-6	52.92	9.43996e-6
2022-08-10T19:28:58	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		-	-	1.077	-	-
2022-08-03T12:34:04	masser	Manual testing	2⁶⁷	2⁶⁹		-	-	3.230	-	-

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