Overview
97 is the integer that comes after 96 and before 98. It is an odd number and a prime number, meaning it has no positive divisors other than 1 and itself. As a prime under 100, 97 is the largest two‑digit prime and occupies a modest but recognizable place in elementary number theory.
Mathematical properties
97 is the 25th prime. It is congruent to 1 modulo 4, so by a classical theorem it can be expressed as a sum of two squares: 97 = 9^2 + 4^2. In base 2 it is written 1100001 and in hexadecimal it appears as 0x61. The nearest primes are 89 (previous) and 101 (next). 97 is also a circular prime because rotating its digits yields 79, which is prime as well.
Representations and examples
- Decimal: 97
- Binary: 1100001
- Hexadecimal: 0x61
- Sum of squares: 97 = 9^2 + 4^2
One widely used appearance of 97 is in computing: the ASCII code for the lowercase letter "a" is 97, so this number frequently appears in programming, text encoding, and examples about character sets.
History, uses and notable facts
Beyond pure mathematics, 97 is the atomic number of the synthetic element berkelium (Bk), a member of the actinide series produced in nuclear reactors and used mainly in research. While the number itself is too small to play a direct role in modern cryptography, its status as a prime makes it a simple illustrative example in teaching primality and modular arithmetic.
Other notable observations: 97 is a happy number (iterating the sum of squares of its digits eventually reaches 1), and because it is 1 mod 4 it factors in the Gaussian integers as (9 + 4i)(9 - 4i). These features make 97 a convenient example across elementary number theory, recreational mathematics, and introductory courses.