M1800577 Mersenne number exponent details

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M1800577

<<<

>>>

is 2 ^1800577 - 1

has 542028 decimal digits

takes 0.098 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	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	2⁶⁷	16.5024	68.6567%	500000	15000000	0.1015	5.0587%	16.6039	70.2423%	1.5856%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	150000	0.0012	2.8703%	0.0119	64.2154%	1.0575%
GPU72	2⁶¹	0.1706	65.5738%	9000	130000	0.0012	1.5545%	0.1718	66.1089%	0.5351%
Difference	+6	+16.3318	+3.0829%	+491000	+14870000	+0.1002	+3.5042%	+16.4321	+4.1334%	+4.1334%

Known prime factors (4 factors, 226.8 bits, 0.01259434% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1800577	40001618633	11	35.219	11108 2² × 2777	-	4	2777	3.570e-9	1.220e-5	2.224e-5
1800577	32864907103375063	17	54.867	9126215403 3 × 59 × 51560539	2014-12-19	59	51560539	0.0017	0.2210	0.4127
1800577	133240083536858280457	21	66.853	36999273992964 2² × 3 × 19 × 9337 × 17380049	2019-09-07	9337	17380049	10.509	0.0752	0.1391
1800577	1050385285256123645519	22	69.831	291680190643367 12577 × 23191555271	2020-04-29	12577	23191555271	132.52	99.394	185.64

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1800577	40001618633 32864907103375063	1314649480358181977288348879	28	90.087
1800577	40001618633 133240083536858280457	5329819008270466733809070955281	31	102.072
1800577	40001618633 1050385285256123645519	42017111598530375795944717355527	32	105.051
1800577	32864907103375063 133240083536858280457	4378922967884780489147210063314043791	37	121.720
1800577	32864907103375063 1050385285256123645519	34520814822694619828107654724316292697	38	124.699
1800577	133240083536858280457 1050385285256123645519	139953423153412628847152113239708553322183	42	136.684
1800577	40001618633 32864907103375063 133240083536858280457	175164006584611495811785892348628163840643557703	48	156.939
1800577	40001618633 32864907103375063 1050385285256123645519	1380888469437843695784882418350141092133797023201	49	159.918
1800577	40001618633 133240083536858280457 1050385285256123645519	55983634593656842316297532819548516620621095450358 39	52	171.903
1800577	32864907103375063 133240083536858280457 1050385285256123645519	45995562507362467152368605885464573887760911333005 26922529	58	191.551
1800577	40001618633 32864907103375063 133240083536858280457 1050385285256123645519	18398969502298266657270384752722331626900621214274 0444532954193882857	69	226.771

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:35:41	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 40001618633	-	-	0.101	-	-	5.059%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-12-19T12:39:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	32864907103375063	54.867	17	0.000	0.207	0.001

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.788 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	17.788 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		255	17.58
50000	5000000	133240083536858280457	2	0.138
50000	5000000	1050385285256123645519	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-09-02T10:30:00	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-30T18:33:44	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-09-07T10:44:38	Chang Chia-Tche	exbpc13	50000	5000000	133240083536858280457	66.853	2	2		2	0.138
2020-03-22T01:03:06	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-29T20:23:18	Greg	azure4	50000	5000000	1050385285256123645519	69.831	1	2	3064799476217919	1	0.069
2020-05-03T06:54:59	Oliver Kruse	IOS-2	50000	5000000						3	0.207
2020-06-01T11:42:41	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.207
2020-06-29T12:56:06	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-07-26T04:36:02	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-10-05T00:37:44	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2020-12-01T12:04:48	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2021-01-29T12:54:25	TJAOI	Manual testing	50000	5000000						222	15.31

Lucas-Lehmer results:
No L-L results for M1800577

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T18:48:30

Oliver Kruse

GTX-2

40001618633

32864907103375063

4D6F447C73B7AD__

2017-11-05T11:11:29

ATH

ec2-1xf

40001618633

32864907103375063

4D6F447C73B7AD__

2019-09-10T12:56:37

mnd9

75211backdoorb

40001618633

32864907103375063

133240083536858280457

5CF32603C61F487E

2019-09-11T07:07:48

kkmrkkblmbrbk

c5.large

40001618633

32864907103375063

133240083536858280457

5CF32603C61F487E

2020-04-30T03:33:52

atrench

Desktop

40001618633

32864907103375063

133240083536858280457

1050385285256123645519

5CF32603C61F487E

2020-04-30T20:08:43

oodaira

com1

40001618633

32864907103375063

133240083536858280457

1050385285256123645519

5CF32603C61F487E

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁵

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-01-29T12:54:25+00:00

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