# 251 (number)

 ← 250 251 252 →
Cardinal two hundred fifty-one
Ordinal 251st
(two hundred fifty-first)
Factorization prime
Prime 54th
Greek numeral ΣΝΑ´
Roman numeral CCLI
Binary 111110112
Ternary 1000223
Quaternary 33234
Quinary 20015
Senary 10556
Octal 3738
Duodecimal 18B12
Vigesimal CB20
Base 36 6Z36

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]${\displaystyle 251=2^{3}+3^{3}+6^{3}=1^{3}+5^{3}+5^{3}.}$

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. ^
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. ^
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. ^