199 is a 3-digit prime number. 199 has 2 factors, 1 and 199. It is the 46th prime number, and the twenty-first and last prime number from 101-200.
Proofs[]
— 199 is divisible by 1.
— 199 is not divisible by 2-198.
- — 199 is divisible by 199.
Therefore, 199 is a prime number.
As an Exponent of Mersenne Number[]
2199 - 1 is divisible by 164,504,919,713, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 193 is the second previous prime number.
- The difference between 199 and 193 is 6. Therefore, they are sexy primes.
- 195 is a composite number. Its prime factorization is 3 × 5 × 13.
- Notably, 195 is a sphenic number since it has exactly three prime factors.
- 197 is the odd number and prime number preceding 199.
- The difference between 199 and 197 is 2. Therefore, they are twin primes.
The numbers after[]
- 201 is a composite number. Its prime factorization is 3 × 67.
- 203 is also a composite number. Its prime factorization is 7 × 29.
- 205 is another composite number. Its prime factorization is 5 × 41.
- 207 is yet another composite number. Its prime factorization is 32 × 23.
- 209 is yet another composite number. Its prime factorization is 11 × 19.
- 211 is the prime number following 199.
Trivia[]
- 199 is a centered triangular number.
- 199 is the largest member of the prime quadruplet (191, 193, 197, 199).
- 199 is the smallest natural number with additive persistence 3.
- Square root of 199 is 14.106735979666
- Cube root of 199 is 5.8382724608