251 (number)

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

← 250 251 252 →
Cardinaltwo hundred fifty-one
Ordinal251st
(two hundred fifty-first)
Factorizationprime
Prime54th
Greek numeralΣΝΑ´
Roman numeralCCLI
Binary111110112
Ternary1000223
Senary10556
Octal3738
Duodecimal18B12
HexadecimalFB16

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. 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. 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. 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. 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. De Koninck, Jean-Marie (2009), Those fascinating numbers, Providence, RI: American Mathematical Society, p. 64, ISBN 978-0-8218-4807-4, MR 2532459.
  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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