M29027293 Mersenne number exponent details

Residue

Status

L-L

C975B5B37F364CED

double-checked

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	2⁷⁵	263.6108	66.6667%	285000	2636250	0.5957	1.9994%	264.2065	67.3331%	0.6665%
PrimeNet	2⁶⁶	0.5088	62.1212%	130000	5000000	0.5700	5.4249%	1.0788	64.1761%	2.0549%
GPU72	2⁷⁰	8.2319	64.2857%	220000	6500000	0.8106	4.0592%	9.0425	65.7354%	1.4497%
Difference	+5	+255.3789	+2.3810%	+65000	-3863750	-0.2149	-2.0598%	+255.1640	+1.5977%	+1.5977%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁵

263.6108

66.6667%

285000

2636250

0.5957

1.9994%

264.2065

67.3331%

0.6665%

PrimeNet

2⁶⁶

0.5088

62.1212%

130000

5000000

0.5700

5.4249%

1.0788

64.1761%

2.0549%

GPU72

2⁷⁰

8.2319

64.2857%

220000

6500000

0.8106

4.0592%

9.0425

65.7354%

1.4497%

Difference

+255.3789

+2.3810%

+65000

-3863750

-0.2149

-2.0598%

+255.1640

+1.5977%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
29027293	41700291740011539369503	23	75.142	718294533010907 13723 × 52342383809	2021-12-12	13723	52342383809	321.07	4,112.1	7,680.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

29027293

41700291740011539369503

75.142

718294533010907
13723 × 52342383809

2021-12-12

13723

52342383809

321.07

4,112.1

7,680.2

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2005-03-20T00:00:00	ANONYMOUS	v4_computers	285000	2636250		-		-	-	0.596	-	-	1.999%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-12-12T11:58:43	ATH	5960X	1000000	28000000	2	7	41700291740011539369503	P+1	23	75.142	4.271

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-01-21T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2005-03-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁸		-	-	2.053	-	-
2012-02-24T15:58:00	LaurV	Manual testing	2⁶⁸	2⁶⁹		-	-	2.060	-	-
2012-02-29T10:08:00	bcp19	Manual testing	2⁶⁹	2⁷⁰		-	-	4.119	-	-
2020-08-17T07:16:04	Sid & Andy	GPU72_TF	2⁷⁰	2⁷¹		-	-	8.238	-	-
2020-08-18T16:05:01	Sid & Andy	GPU72_TF	2⁷¹	2⁷²		-	-	16.48	-	-
2021-01-06T22:40:08	Sid & Andy	Manual testing	2⁷²	2⁷³		-	-	32.95	-	-
2021-09-10T19:51:46	TheJudger	Manual testing	2⁷³	2⁷⁴		-	-	65.90	-	-
2021-10-06T17:00:10	TheJudger	Manual testing	2⁷⁴	2⁷⁵		-	-	131.8	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-04-02T00:00:00	ANONYMOUS	v4_computers	C975B5B37F364CED	28.87
2012-08-20T14:28:00	RMAC9.5	M-Defrancis	C975B5B37F364CED	28.87

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 = 1000000, B2 = 28000000 (P+1 stage 2)

B1 = 1000000 (P+1 stage 1)

B1 = 285000, B2 = 2636250 (P-1 stage 2)

B1 = 285000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷⁵

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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