M523 877 Mersenne number exponent details

≡

M523877

<<<

>>>

is 2 ⁵²³⁸⁷⁷ - 1

has 157703 decimal digits

takes 0.008 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 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
Actual	unknown			10000000	830000000	1.1562	41.6697%	1.1562	41.6697%
Target	2⁴⁴	0.0000	56.8182%	9000	1500000	0.0019	14.6040%	0.0019	63.1244%
Difference	-44	0.0000	-56.8182%	+9991000	+828500000	+1.1543	+27.0658%	+1.1543	-21.4547%

Known prime factors (2 factors, 119.7 bits, 0.02284096% 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
523877	4206732311	10	31.970	4015 5 × 11 × 73	-	11	73	1.021e-9	3.040e-7	4.734e-7
523877	249377078481858336250122041	27	87.688	238011096575969489260 2² × 5 × 101 × 1901 × 19463 × 3184593001	2016-03-24	19463	3184593001	82,102,752	3.6693	6.8525

exponent	prime factors	composite factor	digits	bits*
523877	4206732311 249377078481858336250122041	1049062613672416290428090967567966751	37	119.659

1 Composite Factors:

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17	alpertron	Manual testing	1500000	50000000	12	-	skipped known factor: 4206732311	-	-	0.088	-	-	32.851%
2021-06-06	happy5214	Manual testing	10000000	830000000		-	skipped known factor: 4206732311	-	-	1.156	-	-	41.670%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-06-06	happy5214	Manual testing	5000000	365000000	2	7			-	-	0.485

Trial Factoring results:
No TF results for M523877

ECM factoring results:

Total ECM effort:	16.118 GHz-days
Estimated T-Level:	26.435

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		230	3.703
50000	5000000	249377078481858336250122041	51	0.821
250000	25000000		144	11.59

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-04-19	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-06-26	TJAOI	Manual testing	50000	5000000						99	1.594
2016-03-24	TJAOI	Manual testing	50000	5000000						39	0.628
2016-03-24	TJAOI	Manual testing	50000	5000000	249377078481858336250122041	87.688	51	2		51	0.821
2016-10-21	TJAOI	Manual testing	50000	5000000						91	1.465
2018-10-19	TJAOI	Manual testing	250000	25000000						44	3.542
2020-11-20	TJAOI	Manual testing	250000	25000000						100	8.051

Lucas-Lehmer results:
No L-L results for M523877

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-0

4206732311

249377078481858336250122041

0026DDB5B63E35__

2017-11-03

kkmrkkblmbrbk

c4.xlarge

4206732311

249377078481858336250122041

0026DDB5B63E35__

2020-04-19

Oliver Kruse

AddPrpType5

4206732311

249377078481858336250122041

D37381419945BE__

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 = 10000000, B2 = 830000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=26.44 ~= 71-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

JSON version of this page

Last modified: 2023-10-02T12:12:48+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