Natural numbers are divided into three groups: one, prime numbers, and composite numbers.
The number 1 is considered neither prime nor composite.
Prime numbers up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
There are infinitely many prime numbers. This was proved by Euclid in ancient Greece.
The sieve of Eratosthenes is an algorithm for finding all prime numbers up to a given number N. Steps:
Any composite number can be decomposed into prime factors — that is, represented as a product of prime numbers.
For example: 84 = 2 · 2 · 3 · 7 = 2² · 3 · 7; 360 = 2³ · 3² · 5.
Such a decomposition is unique (up to the order of factors) — this is the fundamental theorem of arithmetic.
A prime number is a natural number greater than 1 that is divisible only by 1 and itself. For example: 2, 3, 5, 7, 11, 13.
No, the number 1 is neither prime nor composite. It has only one divisor — 1. A prime number must have exactly two divisors.
The smallest prime number is 2. It is also the only even prime number.
You need to check whether the number is divisible by any other number besides 1 and itself. It is sufficient to check divisors up to the square root of the number. For example, for the number 97, we check divisors 2, 3, 5, 7 (since √97 ≈ 9.8). None fits, so 97 is prime.
