M27537343 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	4.3355	63.7681%	285000	34496700	2.8844	6.2049%	7.2199	66.0163%	2.2481%
PrimeNet	2⁶⁶	0.5363	62.1212%	130000	4500000	0.4941	5.2811%	1.0304	64.1216%	2.0004%
GPU72	2⁷⁰	8.6773	64.2857%	200000	6000000	0.6926	3.9114%	9.3699	65.6826%	1.3969%
Difference	-1	-4.3419	-0.5176%	+85000	+28496700	+2.1918	+2.2935%	-2.1500	+0.3336%	+0.3336%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

4.3355

63.7681%

285000

34496700

2.8844

6.2049%

7.2199

66.0163%

2.2481%

PrimeNet

2⁶⁶

0.5363

62.1212%

130000

4500000

0.4941

5.2811%

1.0304

64.1216%

2.0004%

GPU72

2⁷⁰

8.6773

64.2857%

200000

6000000

0.6926

3.9114%

9.3699

65.6826%

1.3969%

Difference

-1

-4.3419

-0.5176%

+85000

+28496700

+2.1918

+2.2935%

-2.1500

+0.3336%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27537343	275373431	9	28.037	5 5	-	1	5	1.300e-12	1.635e-6	2.732e-6
27537343	1101493721	10	30.037	20 2² × 5	2008-09-08	4	5	5.217e-12	5.442e-6	1.093e-5
27537343	9770028997657	13	43.151	177396 2² × 3 × 14783	2008-03-11	4	14783	5.946e-8	0.0011	0.0020
27537343	20266382954281	14	44.204	367980 2² × 3 × 5 × 6133	2008-03-11	5	6133	1.404e-7	0.0005	0.0008
27537343	37165933308080405464151	23	74.976	674827874789525 5² × 607² × 613 × 119513	2022-05-16	368449	368449	254.57	0.4946	1.0065

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27537343

275373431

28.037

5
5

1.300e-12

1.635e-6

2.732e-6

27537343

1101493721

30.037

20
2² × 5

2008-09-08

5.217e-12

5.442e-6

1.093e-5

27537343

9770028997657

43.151

177396
2² × 3 × 14783

2008-03-11

14783

5.946e-8

0.0011

0.0020

27537343

20266382954281

44.204

367980
2² × 3 × 5 × 6133

2008-03-11

6133

1.404e-7

0.0005

0.0008

27537343

37165933308080405464151

74.976

674827874789525
5² × 607² × 613 × 119513

2022-05-16

368449

254.57

0.4946

1.0065

exponent	prime factors	composite factor	digits	bits*
27537343	275373431 1101493721	303322105176726751	18	58.074
27537343	275373431 9770028997657	2690406406054299051167	22	71.188
27537343	275373431 20266382954281	5580823408080275108111	22	72.241
27537343	1101493721 9770028997657	10761625594907109211697	23	73.188
27537343	1101493721 20266382954281	22323293571521951569601	23	74.241
27537343	9770028997657 20266382954281	198003149140946908887119617	27	87.356
27537343	275373431 1101493721 9770028997657	2963465763206986789916708222407	31	101.225
27537343	275373431 1101493721 20266382954281	6147241942010243695536862671031	31	102.278
27537343	275373431 37165933308080405464151	10234510571363281276534408372081	32	103.013
27537343	1101493721 37165933308080405464151	40938042173955325181896417095871	32	105.013
27537343	275373431 9770028997657 20266382954281	54524806527747252889090520640695927	35	115.392
27537343	1101493721 9770028997657 20266382954281	218099225516979564133521355901424857	36	117.392
27537343	9770028997657 37165933308080405464151	363112246144931713975681340376494207	36	118.128
27537343	20266382954281 37165933308080405464151	753219037274825187019648878417480431	36	119.181
27537343	275373431 1101493721 37165933308080405464151	11273249131864776736059515462297053203401	41	133.050
27537343	275373431 1101493721 9770028997657 20266382954281	60058732029053411332332317886347460660774367	44	145.429
27537343	275373431 9770028997657 37165933308080405464151	99991465059046369338194021262154041533214217	44	146.165
27537343	275373431 20266382954281 37165933308080405464151	207416510588885501674817376065123436659828761	45	147.217
27537343	1101493721 9770028997657 37165933308080405464151	399965859146848738917980943121572145003374247	45	148.165
27537343	1101493721 20266382954281 37165933308080405464151	829666040095884894874793943201547111386873751	45	149.217
27537343	9770028997657 20266382954281 37165933308080405464151	7358971835762330842777477698769220595670342350167	49	162.332
27537343	275373431 1101493721 9770028997657 37165933308080405464151	11013997091613047007386763990000317168360867297343 1457	54	176.202
27537343	275373431 1101493721 20266382954281 37165933308080405464151	22846798404538739248274632355742915257074259317670 9681	54	177.254
27537343	275373431 9770028997657 20266382954281 37165933308080405464151	20264653230462415447327556034360647526256059179100 90212977	58	190.369
27537343	1101493721 9770028997657 20266382954281 37165933308080405464151	81058612701080506716440298854118259141947618846293 33801407	58	192.369
27537343	275373431 1101493721 9770028997657 20266382954281 37165933308080405464151	22321388291596716541724709202123913499665231823984 05812137718217417	67	220.406

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-05-16T13:09:05	masser	Manual testing	285000	34496700			37165933308080405464151	23	74.976	2.884	50.98	5.769	6.205%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-05-16T13:09:05

masser

Manual testing

285000

34496700

37165933308080405464151

74.976

2.884

50.98

5.769

6.205%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-09-08T23:33:00	Will Edgington	Manual testing	?	?	1101493721	30.037	10	2.24869e-14	52.51	4.63186e-14
2022-07-23T03:18:52	masser	Manual testing	2⁶⁷	2⁶⁹		-	-	3.256	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-09-08T23:33:00

Will Edgington

Manual testing

1101493721

30.037

2.24869e-14

52.51

4.63186e-14

2022-07-23T03:18:52

masser

Manual testing

2⁶⁷

2⁶⁹

3.256

-

-

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