251 (number)

← 250 251 252 →
← 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
Senary	10556
Octal	3738
Duodecimal	18B12
Hexadecimal	FB16

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.). "SequenceA005384(Sophie Germain primes p: 2p+1 is also prime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA006285(Odd numbers not of form p + 2^x (de Polignac numbers))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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. Sloane, N. J. A. (ed.). "SequenceA008917(Numbers that are the sum of 3 positive cubes in more than one way)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
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. Sloane, N. J. A. (ed.). "SequenceA030662(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.