227_(number)

227 (number)

227 (number)

Natural number

227 (two hundred [and] twenty-seven) is the natural number between 226 and 228. It is also a prime number.

Quick Facts ← 226 227 228 →, Cardinal ...

In mathematics

227 is a twin prime and the start of a prime triplet (with 229 and 233).[1] It is a safe prime, as dividing it by two and rounding down produces the Sophie Germain prime 113.[2] It is also a regular prime,[3] a Pillai prime,[4] a Stern prime,[5] and a Ramanujan prime.[6]

227 and 229 form the first twin prime pair for which neither is a cluster prime.

The 227th harmonic number is the first to exceed six.[7] There are 227 different connected graphs with eight edges,[8] and 227 independent sets in a 3 × 4 grid graph.[9]

References

  1. [1]
    Sloane, N. J. A. (ed.). "Sequence A022004 (Initial members of prime triples (p, p+2, p+6))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. [2]
    Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. [3]
    Sloane, N. J. A. (ed.). "Sequence A007703 (Regular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. [4]
    Sloane, N. J. A. (ed.). "Sequence A063980 (Pillai primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. [5]
    Sloane, N. J. A. (ed.). "Sequence A042978 (Stern primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. [6]
    Sloane, N. J. A. (ed.). "Sequence A104272 (Ramanujan primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. [7]
    Sloane, N. J. A. (ed.). "Sequence A002387 (Least k such that H(k) > n, where H(k) is the harmonic number sum_{i=1..k} 1/i)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. [8]
    Sloane, N. J. A. (ed.). "Sequence A002905 (Number of connected graphs with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. [9]
    Sloane, N. J. A. (ed.). "Sequence A051736 (Number of 3 x n (0,1)-matrices with no consecutive 1's in any row or column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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