M18091037 Mersenne number exponent details

Residue

Status

L-L

12676A5384507B0E

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	2⁷³	105.7344	65.7534%	210000	4515000	0.3921	2.5321%	106.1265	66.6206%	0.8672%
PrimeNet	2⁶⁵	0.4033	61.5385%	80000	2400000	0.1821	4.5698%	0.5853	63.2961%	1.7576%
GPU72	2⁶⁹	6.5992	63.7681%	130000	3600000	0.2814	3.4560%	6.8807	65.0203%	1.2522%
Difference	+4	+99.1351	+1.9853%	+80000	+915000	+0.1107	-0.9239%	+99.2458	+1.6003%	-0.3850%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

105.7344

65.7534%

210000

4515000

0.3921

2.5321%

106.1265

66.6206%

0.8672%

PrimeNet

2⁶⁵

0.4033

61.5385%

80000

2400000

0.1821

4.5698%

0.5853

63.2961%

1.7576%

GPU72

2⁶⁹

6.5992

63.7681%

130000

3600000

0.2814

3.4560%

6.8807

65.0203%

1.2522%

Difference

+99.1351

+1.9853%

+80000

+915000

+0.1107

-0.9239%

+99.2458

+1.6003%

-0.3850%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
18091037	54568630375681014871337969747975570063	38	125.359	1508167563188362692291712458163 7 × 421 × 63839 × 98221 × 168737 × 499253 × 968831	2022-02-22	499253	968831	9.618e+9	0.4629	0.8963

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

18091037

54568630375681014871337969747975570063

125.359

1508167563188362692291712458163
7 × 421 × 63839 × 98221 × 168737 × 499253 × 968831

2022-02-22

499253

968831

9.618e+9

0.4629

0.8963

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-10-18T00:00:00	Architects Cubed	v4_computers	210000	4515000		-		-	-	0.392	-	-	2.532%
2022-02-22T17:21:31	Sid & Andy	Magic_8_Ball	1000000	1000000			54568630375681014871337969747975570063	38	125.359	0.882	22.01	1.764	1.877%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-20T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-10-27T00:00:00	Mike Curtis	v4_computers	2¹	2⁶¹		-	-	0.017	-	-
2002-07-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.816	-	-
2014-08-17T10:13:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.826	-	-
2016-06-01T23:45:07	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.652	-	-
2017-09-14T08:54:41	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.305	-	-
2020-03-10T09:59:28	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	6.609	-	-
2021-09-11T16:01:52	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	13.22	-	-
2021-10-08T19:12:17	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	26.44	-	-
2021-11-10T00:54:19	gcardona	Manual testing	2⁷²	2⁷³		-	-	52.87	-	-

ECM factoring results:

Total ECM effort:	0.925 GHz-days
Estimated T-Level:	0.192

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.925

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-08-05T11:15:29	Meracayn	z	50000	5000000						1	0.925

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-04-02T00:00:00	ANONYMOUS	v4_computers	12676A5384507B0E	11.01
2007-04-07T00:00:00	T. Finke	v4_computers	12676A5384507B0E	11.01
2007-04-23T00:00:00	ANONYMOUS	v4_computers	12676A5384507B0E	11.01

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 (P-1 stage 1)

B1 = 210000, B2 = 4515000 (P-1 stage 2)

B1 = 210000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶¹

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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