251 (number)

← 250 251 252 →
← 200 210 220 230 240 250 260 270 280 290 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
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
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] 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, ISBN 9780549210207.
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, ISBN 978-0-8218-4807-4, MR 2532459.