233 is a 3-digit prime number. 233 has 2 factors, 1 and 233. It is the 51st prime number, and the fifth prime number from 201-300.
Proofs[]
— 233 is divisible by 1.
— 233 is not divisible by 2-232.
- — 233 is divisible by 233.
Therefore, 233 is a prime number.
As an Exponent of Mersenne Number[]
2233 - 1 is divisible by 1,399, 135,607, 622,577, etc., and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 229 is the prime number preceding 233.
- The difference between 233 and 229 is 4. Therefore, they are cousin primes.
- 231 is a composite number. Its prime factorization is 3 × 7 × 11.
- Notably, 231 is a sphenic number since it has exactly three prime factors.
The numbers after[]
- 235 is a composite number. Its prime factorization is 5 × 47.
- 237 is also a composite number. Its prime factorization is 3 × 79.
- 239 is the prime number following 233.
- The difference between 239 and 233 is 6. Therefore, they are sexy primes.
Trivia[]
- 233 is a Sophie Germain prime, since 233 × 2 + 1 = 467 is also prime.
- 233 is a Fibonacci prime.
- 233 is a Pillai prime.