M27460523 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	4.3476	63.7681%	285000	34496700	2.8844	6.2028%	7.2320	66.0155%	2.2474%
PrimeNet	2⁶⁶	0.5378	62.1212%	130000	4500000	0.4941	5.2792%	1.0319	64.1209%	1.9997%
GPU72	2⁷⁰	8.7016	64.2857%	200000	6000000	0.6926	3.9099%	9.3942	65.6821%	1.3964%
Difference	-1	-4.3540	-0.5176%	+85000	+28496700	+2.1918	+2.2929%	-2.1622	+0.3334%	+0.3334%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

4.3476

63.7681%

285000

34496700

2.8844

6.2028%

7.2320

66.0155%

2.2474%

PrimeNet

2⁶⁶

0.5378

62.1212%

130000

4500000

0.4941

5.2792%

1.0319

64.1209%

1.9997%

GPU72

2⁷⁰

8.7016

64.2857%

200000

6000000

0.6926

3.9099%

9.3942

65.6821%

1.3964%

Difference

-1

-4.3540

-0.5176%

+85000

+28496700

+2.1918

+2.2929%

-2.1622

+0.3334%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27460523	54921047	8	25.711	1 1	-	1	1	1.628e-13	1.342e-6	2.732e-6
27460523	8567683177	10	32.996	156 2² × 3 × 13	2008-09-08	4	13	2.154e-11	6.027e-6	1.093e-5
27460523	1456341376783	13	40.405	26517 3 × 8839	2008-09-08	3	8839	9.279e-9	0.0007	0.0012
27460523	31248344721682633	17	54.795	568968492 2² × 3 × 47414041	2014-12-15	4	47414041	0.0001	3.4674	6.4761

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27460523

54921047

25.711

1
1

1.628e-13

1.342e-6

2.732e-6

27460523

8567683177

32.996

156
2² × 3 × 13

2008-09-08

2.154e-11

6.027e-6

1.093e-5

27460523

1456341376783

40.405

26517
3 × 8839

2008-09-08

8839

9.279e-9

0.0007

0.0012

27460523

31248344721682633

54.795

568968492
2² × 3 × 47414041

2014-12-15

47414041

0.0001

3.4674

6.4761

exponent	prime factors	composite factor	digits	bits*
27460523	54921047 8567683177	470546130445126319	18	58.707
27460523	54921047 1456341376783	79983793202343851801	20	66.116
27460523	8567683177 1456341376783	12477471513832727479591	23	73.402
27460523	54921047 31248344721682633	1716191809131733806076751	25	80.505
27460523	8567683177 31248344721682633	267725917381057041887165041	27	87.791
27460523	1456341376783 31248344721682633	45508257374165076695600509639	29	95.200
27460523	54921047 8567683177 1456341376783	685275799452368376044808851777	30	99.113
27460523	54921047 8567683177 31248344721682633	14703787691603150707165959913517927	35	113.502
27460523	54921047 1456341376783 31248344721682633	2499361142134616762957680283107472033	37	120.911
27460523	8567683177 1456341376783 31248344721682633	389900331119220322025811236346686643103	39	128.196
27460523	54921047 8567683177 1456341376783 31248344721682633	21413734410714261909334714124524485420132088841	47	153.907

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-05-15T13:51:44	masser	Manual testing	285000	34496700		-	skipped known factor: 54921047 skipped known factor: 8567683177 skipped known factor: 1456341376783	-	-	2.884	-	-	6.203%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T23:32:00	Will Edgington	Manual testing	?	?	1456341376783	40.405	13	3.94510e-9	52.34	8.12308e-9
2008-09-08T23:32:00	Will Edgington	Manual testing	?	?	8567683177	32.996	10	7.03554e-13	52.34	1.44864e-12
2014-12-15T12:40:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	31248344721682633	54.795	17	3.08712e-5	52.34	6.35644e-5
2022-08-10T19:28:57	LordJulius	Manual testing	2¹	2⁶⁵	1456341376783	40.405	13	9.27912e-9	52.34	1.91060e-8
2022-08-10T19:28:57	LordJulius	Manual testing	2¹	2⁶⁵	31248344721682633	54.795	17	0.000	52.34	0.000
2022-08-10T19:28:57	LordJulius	Manual testing	2¹	2⁶⁵	54921047 8567683177	58.707	18	0.003	52.34	0.006
2022-08-10T19:28:57	LordJulius	Manual testing	2¹	2⁶⁵	54921047	25.711	8	1.62817e-13	52.34	3.35244e-13
2022-08-10T19:28:57	LordJulius	Manual testing	2¹	2⁶⁵	8567683177	32.996	10	2.15396e-11	52.34	4.43506e-11
2022-08-10T19:28:57	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.272	-	-
2022-08-10T19:28:58	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	0.544	-	-
2022-08-10T19:28:58	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.089	-	-
2022-07-19T15:23:16	masser	Manual testing	2⁶⁷	2⁶⁹		-	-	3.266	-	-

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