197 is a 3-digit prime number. 197 has 2 factors, 1 and 197. It is the 45th prime number, and the twentieth prime number from 101-200.
Proofs[]
— 197 is divisible by 1.
— 197 is not divisible by 2-196.
- — 197 is divisible by 197.
Therefore, 197 is a prime number.
As an Exponent of Mersenne Number[]
2197 - 1 is divisible by 7,487, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 193 is the prime number preceding 197.
- The difference between 197 and 193 is 4. Therefore, they are cousin primes.
- 195 is the odd number preceding 197. It is a composite number; its prime factorization is 3 × 5 × 13.
- Notably, 195 is a sphenic number since it has exactly three prime factors.
The numbers after[]
- 199 is the odd number and prime number following 197.
- The difference between 199 and 197 is 2. Therefore, they are twin primes.
- 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[]
- 197 is part of the prime quadruplet (191, 193, 197, 199).
- 197 is the sum of seven consecutive prime numbers (17 + 19 + 23 + 29 + 31 + 37 + 41), as well as the sum of the first twelve prime numbers (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37).
- 197 is a centered heptagonal number.
- 197 is currently the number of countries in the world.