277 (number)

Last updated

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
Senary 11416
Octal 4258
Duodecimal 1B112
Hexadecimal 11516

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]

Related Research Articles

68 (sixty-eight) is the natural number following 67 and preceding 69. It is an even number.

103 is the natural number following 102 and preceding 104.

109 is the natural number following 108 and preceding 110.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number.

2000 is a natural number following 1999 and preceding 2001.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.

5000 is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic numeral in the English language.

138 is the natural number following 137 and preceding 139.

193 is the natural number following 192 and preceding 194.

251 is the natural number between 250 and 252. It is also a prime number.

501 is the natural number following 500 and preceding 502.

168 is the natural number following 167 and preceding 169.

288 is the natural number following 287 and preceding 289. Because 288 = 2 · 12 · 12, it may also be called "two gross" or "two dozen dozen".

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA007703(Regular primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA016088(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.). "SequenceA006450(Primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Fernandez, Neil (1999), An order of primeness, F(p), archived from the original on 2012-07-10, retrieved 2013-09-11.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA002585(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.). "SequenceA000124(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.). "SequenceA001608(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.). "SequenceA002478(Bisection of A000930)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  10. ↑ Sloane, N. J. A. (ed.). "SequenceA051894(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.). "SequenceA118312(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.). "SequenceA046976(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.). "SequenceA006378(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.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.