97 is a prime number from 1-100. 97 has 2 factors, 1 and 97. It is the 25th prime number and the final prime predecessor of 100.
Proofs[]
— 97 is divisible by 1.
— 97 is not divisible by 2-96.
- — 97 is divisible by 97.
Therefore, 97 is a prime number.
As an Exponent of Mersenne Number[]
297 - 1 is divisible by 11,447, and is therefore not a prime number.
Relationship with other odd numbers[]
The numbers before[]
- 89 is the previous prime number.
- 91 is a composite number; its prime factorization is 7 * 13.
- 93 is also a composite number; its prime factorization is 3 * 31.
- 95 is yet another composite number; its prime factorization is 5 * 19.
The numbers after[]
- 99 is the odd integer following 97. It is a composite number; its prime factorization is 32 * 11.
- 101 is the prime number following 97.
- The difference between 101 and 97 is 4. Therefore, they are cousin primes.
- 103 is the prime number following 101.
- The difference between 103 and 97 is 6. Therefore, they are sexy primes.
In science[]
- 97 is the atomic number of berkelium.
Trivia[]
- 97 is a Proth prime, since it is of the form 3 × 2n + 1. In this case, n = 5.
- 97 is a self number as well as a self prime.
- 97 is an emirp with 79.
- 97 is the largest two-digit number such that the sum of its digits is equal to a square (9 + 7 = 16 = 42).
- 97 is the amount of primes less than 29 = 512.
- 97, 907, 9,007, 90,007, and 900,007 are all prime. However, 9,000,007 is not prime.
- 97 is an isolated prime, since 97 - 2 = 95 and 97 + 2 = 99 are not prime.
- 97 is a Pierpont prime, since it is of the form 2u × 3v + 1. In this case, u and v are equal to 5 and 1 respectively.