277 is the 59thprime number, and aregular prime.[1]It is the smallest primep such that thesum of the inverses of the primes up top is greater than two.[2]Since 59 is itself prime, 277 is asuper-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 theEuclid number 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1.[5]
As a member of thelazy caterer's sequence, 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts.[6]277 is also aPerrin number, and as such counts the number ofmaximal independent sets in anicosagon.[7][8] There are 277 ways to tile a 3 × 8 rectangle with integer-sided squares,[9] and 277 degree-7monic polynomials with integer coefficients and all roots in theunit disk.[10]On an infinitechessboard, there are 277 squares that aknight can reach from a given starting position in exactly six moves.[11]
