M23517601 Mersenne number exponent details

Residue

Status

L-L

4B6CEAEA782757FB

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	2⁷⁰	10.1605	64.2857%	1200000	79200000	6.4094	7.4806%	16.5699	66.9574%	2.6716%
PrimeNet	2⁶⁶	0.6280	62.1212%	100000	3600000	0.3419	4.7679%	0.9699	63.9273%	1.8060%
GPU72	2⁷⁰	10.1605	64.2857%	160000	4500000	0.4663	3.4851%	10.6268	65.5304%	1.2447%
Difference	-	-	-	+1040000	+74700000	+5.9431	+3.9955%	+5.9431	+1.4270%	+1.4270%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

10.1605

64.2857%

1200000

79200000

6.4094

7.4806%

16.5699

66.9574%

2.6716%

PrimeNet

2⁶⁶

0.6280

62.1212%

100000

3600000

0.3419

4.7679%

0.9699

63.9273%

1.8060%

GPU72

2⁷⁰

10.1605

64.2857%

160000

4500000

0.4663

3.4851%

10.6268

65.5304%

1.2447%

Difference

+1040000

+74700000

+5.9431

+3.9955%

+5.9431

+1.4270%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
23517601	273713500011802341154177183	27	87.823	5819332933061546991 3 × 211 × 587 × 415559 × 37687619	2021-05-07	415559	37687619	2,403,266	2.8771	4.5104
23517601	287344583294713977269086586924951	33	107.824	6109138923113670847402475 5² × 7 × 83 × 1193 × 24749 × 1034597 × 13768751	2021-05-07	1034597	13768751	6.968e+9	2.0328	2.4764

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

23517601

273713500011802341154177183

87.823

5819332933061546991
3 × 211 × 587 × 415559 × 37687619

2021-05-07

415559

37687619

2,403,266

2.8771

4.5104

23517601

287344583294713977269086586924951

107.824

6109138923113670847402475
5² × 7 × 83 × 1193 × 24749 × 1034597 × 13768751

2021-05-07

1034597

13768751

6.968e+9

2.0328

2.4764

exponent	prime factors	composite factor	digits	bits*
23517601	273713500011802341154177183 287344583294713977269086586924951	78650091603029033018091227770166444001988216065464 577593033	59	195.647

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-03-08T00:00:00	ANONYMOUS	v4_computers	340000	340000		-		-	-	0.400	-	-	1.743%
2021-05-07T04:37:17	firejuggler	Maison	1200000	79200000			273713500011802341154177183 287344583294713977269086586924951	59	195.647	6.409	38.15	12.82	7.481%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-05-13T15:03:46	firejuggler	Maison	500000	23500000	6	5			-	-	2.338

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-09-10T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2003-07-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.007	-	-
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁷		-	-	1.263	-	-
2016-06-10T01:52:44	VictordeHollander	Manual testing	2⁶⁷	2⁶⁸		-	-	1.271	-	-
2018-01-05T17:22:17	VictordeHollander	Manual testing	2⁶⁸	2⁶⁹		-	-	2.542	-	-
2018-08-26T21:57:25	ramgeis	Manual testing	2⁶⁹	2⁷⁰		-	-	5.084	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2004-12-13T00:00:00	ANONYMOUS	v4_computers	4B6CEAEA782757FB	19.08
2010-08-05T16:25:00	gkramer	OverLord	4B6CEAEA782757FB	19.08

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 = 1200000, B2 = 79200000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 340000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁰

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

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