M1854563 Mersenne number exponent details

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M1854563

<<<

>>>

is 2 ^1854563 - 1

has 558280 decimal digits

takes 0.101 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	16.0221	68.6567%	500000	15000000	0.1015	5.0767%	16.1235	70.2479%	1.5912%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0245%	0.0117	64.2722%	1.1143%
GPU72	2⁶¹	0.1656	65.5738%	9000	150000	0.0013	1.6318%	0.1669	66.1355%	0.5618%
Difference	+6	+15.8564	+3.0829%	+491000	+14850000	+0.1002	+3.4449%	+15.9566	+4.1124%	+4.1124%

Known prime factors (4 factors, 177.2 bits, 0.00955238% 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
1854563	122401159	9	26.867	33 3 × 11	-	3	11	4.855e-12	2.703e-7	4.803e-7
1854563	39335281231	11	35.195	10605 3 × 5 × 7 × 101	2008-07-15	7	101	3.197e-9	9.535e-7	1.121e-6
1854563	826807971632431	15	49.555	222911805 3 × 5 × 1217 × 12211	2014-05-06	1217	12211	5.291e-5	0.0001	0.0002
1854563	53574278631363551729	20	65.538	14443909058728 2³ × 5821 × 310168121	2017-12-16	5821	310168121	4.5340	1.3297	2.4828

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1854563	122401159 39335281231	4814684012265346729	19	62.062
1854563	122401159 826807971632431	101202253998248676387529	24	76.422
1854563	39335281231 826807971632431	32522724088194343545202561	26	84.750
1854563	122401159 53574278631363551729	6557553797067832481986053911	28	92.405
1854563	39335281231 53574278631363551729	2107359316712639084263231298399	31	100.733
1854563	122401159 39335281231 826807971632431	3980819122232205867176962356168199	34	111.617
1854563	826807971632431 53574278631363551729	44295640646868389777519914242523199	35	115.093
1854563	122401159 39335281231 53574278631363551729	257943222795075093862518172009112444441	39	127.600
1854563	122401159 826807971632431 53574278631363551729	5421837753824200629232189648865446641987641	43	141.960
1854563	39335281231 826807971632431 53574278631363551729	1742381482151882871342871348432652371706777969	46	150.288
1854563	122401159 39335281231 826807971632431 53574278631363551729	21326951283552827748461533943604948374100843156126 6071	54	177.155

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:36:11	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 122401159 skipped known factor: 39335281231 skipped known factor: 826807971632431	-	-	0.101	-	-	5.077%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	39335281231	35.195	11	7.29227e-10	0.215	1.55825e-9
2014-05-06T12:36:00	TJAOI	Manual testing	?	?	826807971632431	49.555	15	1.24728e-5	0.215	2.66425e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.815 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:	19.815 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.638	0.002%
25	50000	0.979	37.570%
30	250000	0.062	93.976%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.283
50000	5000000	53574278631363551729	2	0.138
50000	6600000		223	17.39

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T19:15:40	ATH	ec2-1xe	50000	5000000	53574278631363551729	65.538	2	2		2	0.138
2018-10-26T22:41:25	Ducho_YYZ	Dutch	50000	5000000						3	0.208
2020-06-12T16:09:10	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.208
2020-07-07T05:28:59	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2020-08-09T07:38:06	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.208
2020-10-13T21:55:31	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2020-12-20T18:29:20	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2021-03-21T07:15:42	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-07-09T11:24:37	TJAOI	Manual testing	50000	6600000						223	17.39

Lucas-Lehmer results:
No L-L results for M1854563

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T07:04:26

Oliver Kruse

GTX-2

122401159

39335281231

826807971632431

83526A79230D9D__

2017-11-07T02:52:36

kkmrkkblmbrbk

c4.xlarge

122401159

39335281231

826807971632431

83526A79230D9D__

2017-12-19T03:34:24

Oliver Kruse

GTX-0

122401159

39335281231

826807971632431

53574278631363551729

7D8124FD1D3CB3__

2017-12-19T10:54:21

kkmrkkblmbrbk

c4.xlarge

122401159

39335281231

826807971632431

53574278631363551729

7D8124FD1D3CB3__

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

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-07-09T11:24:37+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