# 277 (number)

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

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | two hundred seventy-seven | |||

Ordinal | 277th (two hundred seventy-seventh) | |||

Factorization | prime | |||

Prime | yes | |||

Greek numeral | ΣΟΖ´ | |||

Roman numeral | CCLXXVII | |||

Binary | 100010101_{2} | |||

Ternary | 101021_{3} | |||

Quaternary | 10111_{4} | |||

Quinary | 2102_{5} | |||

Senary | 1141_{6} | |||

Octal | 425_{8} | |||

Duodecimal | 1B1_{12} | |||

Hexadecimal | 115_{16} | |||

Vigesimal | DH_{20} | |||

Base 36 | 7P_{36} |

## 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]}

- [math]\displaystyle{ \sec x = 1 + \frac{1}{2} x^2 + \frac{5}{24} x^4 + \frac{61}{720} x^6 + \frac{277}{8064} x^8 + \cdots }[/math]

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

- ↑ Sloane, N. J. A., ed. "Sequence A007703 (Regular primes)". OEIS Foundation. https://oeis.org/A007703.
- ↑ Sloane, N. J. A., ed. "Sequence A016088 (a(n) = smallest prime p such that Sum_{ primes q = 2, ..., p} 1/q exceeds n)". OEIS Foundation. https://oeis.org/A016088.
- ↑ Sloane, N. J. A., ed. "Sequence A006450 (Primes with prime subscripts)". OEIS Foundation. https://oeis.org/A006450.
- ↑ Fernandez, Neil (1999),
*An order of primeness, F(p)*, http://borve.org/primeness/FOP.html. - ↑ Sloane, N. J. A., ed. "Sequence A002585 (Largest prime factor of 1 + (product of first n primes))". OEIS Foundation. https://oeis.org/A002585.
- ↑ 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)". OEIS Foundation. https://oeis.org/A000124.
- ↑ Sloane, N. J. A., ed. "Sequence A001608 (Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3))". OEIS Foundation. https://oeis.org/A001608.
- ↑ "The number of maximal independent sets in connected graphs",
*Journal of Graph Theory***11**(4): 463–470, 1987, doi:10.1002/jgt.3190110403. - ↑ Sloane, N. J. A., ed. "Sequence A002478 (Bisection of A000930)". OEIS Foundation. https://oeis.org/A002478.
- ↑ Sloane, N. J. A., ed. "Sequence A051894 (Number of monic polynomials with integer coefficients of degree n with all roots in unit disc)". OEIS Foundation. https://oeis.org/A051894.
- ↑ 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)". OEIS Foundation. https://oeis.org/A118312.
- ↑ Sloane, N. J. A., ed. "Sequence A046976 (Numerators of Taylor series for sec(x) = 1/cos(x))". OEIS Foundation. https://oeis.org/A046976.
- ↑ 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)". OEIS Foundation. https://oeis.org/A006378.

ca:Nombre 270#Nombres del 271 al 279

Original source: https://en.wikipedia.org/wiki/277 (number).
Read more |