251 is a 3-digit prime number. 251 has 2 factors, 1 and 251. It is the 54th prime number, and the eighth prime number from 201-300.
Proofs[]
— 251 is divisible by 1.
— 251 is not divisible by 2-250.
- — 251 is divisible by 251.
Therefore, 251 is a prime number.
As an Exponent of Mersenne Number[]
2251 - 1 is divisible by 503, 54,217, etc., and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 241 is the prime number preceding 251.
- 243 is a composite number. It is the fifth power of 3, equal to 35.
- 245 is a composite number. Its prime factorization is 5 × 72.
- 247 is a composite number. Its prime factorization is 13 × 19.
- 249 is a composite number. Its prime factorization is 3 × 83.
The numbers after[]
- 253 is a composite number. Its prime factorization is 11 × 23.
- 255 is a composite number. Its prime factorization is 3 × 5 × 17.
- Notably, 255 is a sphenic number, since it has exactly three prime factors.
- 257 is the prime number following 251.
- The difference between 257 and 251 is 6. Therefore, they are sexy primes.
Trivia[]
- 251 is the sum of three consecutive primes (79 + 83 + 89) and seven consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47).
- 251 is a Chen prime, since 251 + 2 = 253 is a semiprime.
- 251 is the smallest number that can be represented in more than one way as a sum of three cubes: 251 = 23 + 33 + 63 = 13 + 53 + 53.