67 is a prime number from 1-100. 67 has 2 factors, 1 and 67. It is the nineteenth prime number, and the nineteenth prime number from 1-100.
Proofs[]
— 67 is divisible by 1.
— 67 is not divisible by 2-66.
- — 67 is divisible by 67.
Therefore, 67 has two factors and is prime.
As an Exponent of Mersenne Number[]
267 - 1 is divisible by 193,707,721, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 61 is the previous prime number.
- The difference between 67 and 61 is 6. Therefore, they are sexy primes.
- 63 is a composite number. Its prime factorization is 32 * 7.
- 65 is also a composite number. Its prime factorization is 5 * 13.
The numbers after[]
- 69, the next odd number, is also a composite number. Its prime factorization is 3 * 23.
- 71 is the next prime number.
- The difference between 71 and 67 is 4. Therefore, they are cousin primes.
- 73, the odd number following 71, is also a prime number.
- The difference between 73 and 67 is 6. Therefore, they are sexy primes.
In science[]
- 67 is the atomic number of holmium.
Trivia[]
- 67 is a Chen prime, since 67 + 2 = 69 is a semiprime.
- 67 is a super-prime, since its position in the sequence of all primes is 19, which is a prime number.
- 67 is the sum of five consecutive primes (7 + 11 + 13 + 17 + 19).
- 67 is an isolated prime, since 65 and 69 are not prime, i.e. 67 is not part of a twin prime pair.