# 277 (number)

277 (two hundred [and] seventy-seven) is the natural number following 276 and preceding 278.

Short description: Natural number
 ← 276 277 278 →
Cardinaltwo hundred seventy-seven
Ordinal277th
(two hundred seventy-seventh)
Factorizationprime
Primeyes
Greek numeralΣΟΖ´
Roman numeralCCLXXVII
Binary1000101012
Ternary1010213
Quaternary101114
Quinary21025
Senary11416
Octal4258
Duodecimal1B112
VigesimalDH20
Base 367P36

## Mathematical properties

277 is the 59th prime number, and is a regular prime.[1] It is the smallest prime p such that the sum of the inverses of the primes up to p is greater than two.[2] Since 59 is itself prime, 277 is a super-prime.[3] 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.[4] It is the largest prime factor of the Euclid number 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.[5]

As a member of the lazy caterer's sequence, 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts.[6] 277 is also a Perrin number, and as such counts the number of maximal independent sets in an icosagon.[7][8] There are 277 ways to tile a 3 × 8 rectangle with integer-sided squares,[9] and 277 degree-7 monic polynomials with integer coefficients and all roots in the unit disk.[10] On an infinite chessboard, there are 277 squares that a knight can reach from a given starting position in exactly six moves.[11]

277 appears as the numerator of the fifth term of the Taylor series for the secant function:[12]

$\displaystyle{ \sec x = 1 + \frac{1}{2} x^2 + \frac{5}{24} x^4 + \frac{61}{720} x^6 + \frac{277}{8064} x^8 + \cdots }$

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.[13]

## References

1. Sloane, N. J. A., ed. "Sequence A007703 (Regular primes)". OEIS Foundation.
2. Sloane, N. J. A., ed. "Sequence A006450 (Primes with prime subscripts)". OEIS Foundation.
3. Fernandez, Neil (1999), An order of primeness, F(p) .
4. "The number of maximal independent sets in connected graphs", Journal of Graph Theory 11 (4): 463–470, 1987, doi:10.1002/jgt.3190110403 .
5. Sloane, N. J. A., ed. "Sequence A002478 (Bisection of A000930)". OEIS Foundation.

ca:Nombre 270#Nombres del 271 al 279