167 is a 3-digit prime number. 167 has 2 factors, 1 and 167. It is the 39th prime number, and the fourteenth prime number from 101-200.
Proofs[]
— 167 is divisible by 1.
— 167 is not divisible by 2-166.
- — 167 is divisible by 167.
Therefore, 167 is a prime number.
As an Exponent of Mersenne Number[]
2167 - 1 is divisible by 2,349,023, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 161 is a composite number. Its prime factorization is 7 × 23.
- 163 is the previous prime number.
- The difference between 167 and 163 is 4. Therefore, they are cousin primes.
- 165 is a composite number. Its prime factorization is 3 × 5 × 11.
- Notably, 165 is a sphenic number due to having exactly three prime factors, which is rare among small positive integers.
The numbers after[]
- 169 is a composite number. It is the thirteenth positive square number, equal to 132.
- 171 is also a composite number. Its prime factorization is 32 × 19.
- 173 is the prime number following 167.
- The difference between 173 and 167 is 6. Therefore, they are sexy primes.
- 175 is a composite number. Its prime factorization is 52 × 7.
- 177 is also a composite number. Its prime factorization is 3 × 59.
- 179 is the prime number following 173.
Trivia[]
- 167 is the smallest number that requires six terms when expressed as a sum of square numbers using the greedy algorithm: 167 = 144 + 16 + 1 + 1 + 1 + 1.
- By Lagrange's four-square theorem, its non-greedy expression as a sum of squares could be shorter: 167 = 121 + 36 + 9 + 1.
- 167 is a Chen prime, since 167 + 2 = 169 is a semiprime.
- 167 is an emirp, since its reverse, 761, is also prime.
- 167 is an isolated prime, since it is not part of a twin prime pair.
- 167 is a strictly non-palindromic number, since it is not palindromic in any base from base 2 to 165.
- 167 is a safe prime, since is also prime.
