251 (number) explained

Number:	251
Prime:	54th

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 = 2 ^{3} + 3 ^{3} + 6 ^{3} = 1 ^{3} + 5 ^{3} + 5 ^{3.} Every 5 × 5 matrix has exactly 251 square submatrices.^[6]

Notes and References

1. Sophie Germain primes p: 2p+1 is also prime.
2. Odd numbers not of form p + 2^x (de Polignac numbers).
3. .
4. Numbers that are the sum of 3 positive cubes in more than one way.
5. .
6. Number of combinations of n things from 1 to n at a time, with repeats allowed.