251 (number)

Short description: Natural number

| <- 250  | 251 |  252 ->

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← 250 251 252 253 254 255 256 257 258 259 →

List of numbers — Integers

← 0 100 200 300 400 500 600 700 800 900 →

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
Hexadecimal| FB16
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]251=23+33+63=13+53+53.

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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