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251 (number)

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Short description: Natural number
← 250 251 252 →
Cardinaltwo hundred fifty-one
Ordinal251st
(two hundred fifty-first)
Factorizationprime
Prime54th
Greek numeralΣΝΑ´
Roman numeralCCLI
Binary111110112
Ternary1000223
Quaternary33234
Quinary20015
Senary10556
Octal3738
Duodecimal18B12
HexadecimalFB16
VigesimalCB20
Base 366Z36

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

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][math]\displaystyle{ 251 = 2^3 + 3^3 + 6^3 = 1^3 + 5^3 + 5^3. }[/math]

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)". OEIS Foundation. https://oeis.org/A005384. 
  2. ↑ Sloane, N. J. A., ed. "Sequence A006285 (Odd numbers not of form p + 2^x (de Polignac numbers))". OEIS Foundation. https://oeis.org/A006285. 
  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, https://books.google.com/books?id=DirKAJqYGGsC&pg=PA14 .
  4. ↑ Sloane, N. J. A., ed. "Sequence A008917 (Numbers that are the sum of 3 positive cubes in more than one way)". OEIS Foundation. https://oeis.org/A008917. 
  5. ↑ De Koninck, Jean-Marie (2009), Those fascinating numbers, Providence, RI: American Mathematical Society, p. 64, ISBN 978-0-8218-4807-4, https://books.google.com/books?id=xdfTAwAAQBAJ&pg=PA64 .
  6. ↑ Sloane, N. J. A., ed. "Sequence A030662 (Number of combinations of n things from 1 to n at a time, with repeats allowed)". OEIS Foundation. https://oeis.org/A030662. 



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