251 (number)

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

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

References

1.
2. 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 .
3. De Koninck, Jean-Marie (2009), Those fascinating numbers, Providence, RI: American Mathematical Society, p. 64, ISBN 978-0-8218-4807-4 .