277 (number)

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

← 276 277 278 →
Cardinal two hundred seventy-seven
Ordinal 277th
(two hundred seventy-seventh)
Factorization prime
Prime yes
Greek numeral ΣΟΖ´
Roman numeral CCLXXVII
Binary 1000101012
Ternary 1010213
Quaternary 101114
Quinary 21025
Senary 11416
Octal 4258
Duodecimal 1B112
Hexadecimal 11516
Vigesimal DH20
Base 36 7P36

Mathematical properties[edit]

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]

References[edit]

  1. ^ Sloane, N.J.A. (ed.). "Sequence A007703 (Regular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  2. ^ Sloane, N.J.A. (ed.). "Sequence A016088 (a(n) = smallest prime p such that Sum_{ primes q = 2, ..., p} 1/q exceeds n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  3. ^ Sloane, N.J.A. (ed.). "Sequence A006450 (Primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  4. ^ Fernandez, Neil (1999), An order of primeness, F(p) .
  5. ^ Sloane, N.J.A. (ed.). "Sequence A002585 (Largest prime factor of 1 + (product of first n primes))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  6. ^ Sloane, N.J.A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  7. ^ Sloane, N.J.A. (ed.). "Sequence A001608 (Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  8. ^ 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 .
  9. ^ Sloane, N.J.A. (ed.). "Sequence A002478 (Bisection of A000930)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  10. ^ Sloane, N.J.A. (ed.). "Sequence A051894 (Number of monic polynomials with integer coefficients of degree n with all roots in unit disc)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  11. ^ Sloane, N.J.A. (ed.). "Sequence A118312 (Number of squares on infinite chessboard that a knight can reach in n moves from a fixed square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  12. ^ Sloane, N.J.A. (ed.). "Sequence A046976 (Numerators of Taylor series for sec(x) = 1/cos(x))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  13. ^ Sloane, N.J.A. (ed.). "Sequence A006378 (Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.