277 (number)

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

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]

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]

Two hundred and seventy-seven is also:

• The length of the Grand Canyon in river miles, beginning at Lees Ferry (mile 0) and ending at the Grand Wash Cliffs (mile 277).^[14]

References