277 (two hundred
ndseventy-seven) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
following
276 and preceding
278
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Year 278 ( CCLXXVIII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Lupus (or, less frequently, year 1031 '' ...
.
Mathematical properties
277 is the 59th
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
, and is a
regular prime
In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli nu ...
.
It is the smallest prime ''p'' such that the
sum of the inverses of the primes up to ''p'' is greater than two.
Since 59 is itself prime, 277 is a
super-prime. 59 is also a super-prime (it is the 17th prime), as is 17 (the 7th prime). However, 7 is the fourth prime number, and 4 is not prime. Thus, 277 is a super-super-super-prime but not a super-super-super-super-prime. It is the largest prime factor of the
Euclid number 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.
As a member of the
lazy caterer's sequence
The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cu ...
, 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts.
277 is also a
Perrin number, and as such counts the number of
maximal independent sets in an
icosagon. There are 277 ways to tile a 3 × 8 rectangle with integer-sided squares, and 277 degree-7
monic polynomial
In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1. Therefore, a monic polynomial has the form:
:x^n+c_x^+\c ...
s with integer coefficients and all roots in the
unit disk.
On an infinite
chessboard, there are 277 squares that a
knight
A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the church or the country, especially in a military capacity. Knighthood finds origins in the Gr ...
can reach from a given starting position in exactly six moves.
277 appears as the numerator of the fifth term of the
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...
for the
secant function
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in al ...
:
:
Since no number added to the sum of its digits generates 277, it is a
self number. The next prime self number is not reached until 367.
References
{{DEFAULTSORT:277 (Number)
Integers
ca:Nombre 270#Nombres del 271 al 279