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# 251 (number)

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 Title: 251 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 251 (number)

 ← 250 251 252 →
Cardinal two hundred fifty-one
Ordinal 251st
(two hundred and fifty-first)
Factorization 251
Prime 54th
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] Every 5 × 5 matrix has exactly 251 square submatrices.[2] 251 is a de Polignac number, meaning that it is odd and cannot be formed by adding a power of two to a prime number.[3][4] It is the smallest number that can be formed in more than one way by summing three positive cubes:[5][6]

251 = 2^3 + 3^3 + 6^3 = 1^3 + 5^3 + 5^3.

## References

1. ^ "Sloane's A005384 : Sophie Germain primes p: 2p+1 is also prime", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ "Sloane's 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.
3. ^ "Sloane's A006285 : Odd numbers not of form p + 2^x (de Polignac numbers)", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ 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, .
5. ^ "Sloane's A008917 : Numbers that are the sum of 3 positive cubes in more than one way", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ De Koninck, Jean-Marie (2009), Those fascinating numbers, Providence, RI: American Mathematical Society, p. 64, .
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