Mathematical properties
277 is the 59th prime number, and 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]
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]