277 (number)

Mathematical properties

277 is the 59th prime number, and a regular prime. It is the smallest prime p such that the sum of the inverses of the primes up to p is greater than two. Since 59 is itself prime, 277 is a super-prime. 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.{{citation | access-date = 2013-09-11 | archive-date = 2012-07-10 | archive-url = https://web.archive.org/web/20120710231820/http://www.borve.org/primeness/FOP.html | url-status = live

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. 277 is also a Perrin number, and as such counts the number of maximal independent sets in an icosagon.{{citation On an infinite chessboard, there are 277 squares that a knight can reach from a given starting position in exactly six moves.

277 appears as the numerator of the fifth term of the Taylor series for the secant function: :\sec x = 1 + \frac{1}{2} x^2 + \frac{5}{24} x^4 + \frac{61}{720} x^6 + \frac{277}{8064} x^8 + \cdots

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.

References

ca:Nombre 270#Nombres del 271 al 279

References

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