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]
^Füredi, Z. (1987), "The number of maximal independent sets in connected graphs", Journal of Graph Theory, 11 (4): 463–470,
doi:
10.1002/jgt.3190110403.