251 (number)

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.^[2]
• 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.^[3][4]
• the first of four consecutive primes in an arithmetic progression, the common difference being 6: 251, 257, 263, 269.
• the smallest number that can be formed in more than one way by summing three positive cubes:^[5][6]${\displaystyle 251=2^{3}+3^{3}+6^{3}=1^{3}+5^{3}+5^{3}.}$

Every 5 × 5 matrix has exactly 251 square submatrices.^[7]