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]
Every 5 × 5 matrix has exactly 251 square submatrices.[6]
References
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ De Koninck, Jean-Marie (2009), Those fascinating numbers, Providence, RI: American Mathematical Society, p. 64, ISBN 978-0-8218-4807-4, MR 2532459.
- ^ 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.