257 is a 3-digit prime number. 257 has 2 factors, 1 and 257. It is the 55th prime number, and the ninth prime number from 201-300.
Proofs[]
— 257 is divisible by 1.
— 257 is not divisible by 2-256.
- — 257 is divisible by 257.
Therefore, 257 is a prime number.
As an Exponent of Mersenne Number[]
2257 - 1 is divisible by 535,006,138,814,359 and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- The prime number preceding 257 is 251.
- The difference between 257 and 251 is 6. Therefore, they are sexy primes.
- 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 3 prime factors.
The numbers after[]
- 259, the odd number following 257, is a composite number. Its prime factorization is 7 × 37.
- 261 is a composite number. Its prime factorization is 32 × 29.
- 263 is the prime number following 257.
- The difference between 263 and 257 is 6. Therefore, they are sexy primes.
Trivia[]
- 257 is the fourth Fermat prime, equal to 223 + 1.
- 257 is the third Sierpinski prime of the first kind, of the form nn + 1, specifically for n = 4.
- 257 is a balanced prime.
- 257 is an isolated prime, meaning it is not part of a twin prime pair.