251_(number)

251 (number)

251 (number)

Natural number

251 (two hundred [and] fifty-one) is the natural number between 250 and 252. It is also a prime number.

Quick Facts ← 250 251 252 →, Cardinal ...

In mathematics

251 is:

  • a Sophie Germain prime.[1]
  • the sum of three consecutive primes (79 + 83 + 89) and seven consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47).
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • a de Polignac number, meaning that it is odd and cannot be formed by adding a power of two to a prime number.[2][3]
  • the smallest number that can be formed in more than one way by summing three positive cubes:[4][5]

Every 5 × 5 matrix has exactly 251 square submatrices.[6]

References

  1. [1]
    Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. [2]
    Sloane, N. J. A. (ed.). "Sequence A006285 (Odd numbers not of form p + 2^x (de Polignac numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. [3]
    Kozek, Mark Robert (2007), Applications of Covering Systems of Integers and Goldbach's Conjecture for Monic Polynomials, PhD dissertation, University of South Carolina, p. 14, ISBN 9780549210207.
  4. [4]
    Sloane, N. J. A. (ed.). "Sequence A008917 (Numbers that are the sum of 3 positive cubes in more than one way)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. [5]
    De Koninck, Jean-Marie (2009), Those fascinating numbers, Providence, RI: American Mathematical Society, p. 64, ISBN 978-0-8218-4807-4, MR 2532459.
  6. [6]
    Sloane, N. J. A. (ed.). "Sequence A030662 (Number of combinations of n things from 1 to n at a time, with repeats allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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