Why is 1 not considered a prime number?
Because if 1 were prime, the Fundamental Theorem of Arithmetic (unique prime factorization) would break, as you could multiply by 1 infinitely.
Check if a number is prime and list factors if not.
Determines whether an integer is prime or composite, testing trial divisibility up to sqrt(n) with 6k ± 1 primality optimizations and prime factorizations.
Primality Test: Check divisibility by 2, 3, and all integers 6k ± 1 <= sqrt(n)
A prime number is an integer strictly greater than 1 that has no positive divisors other than 1 and itself.
Inputs: Integer n = 97
Summary: Number = 97 | Status = PRIME | Factors = 1 and 97 only
Because if 1 were prime, the Fundamental Theorem of Arithmetic (unique prime factorization) would break, as you could multiply by 1 infinitely.
Because if n had a factor larger than sqrt(n), its corresponding factor pair would have to be smaller than sqrt(n), which would have already been detected.
Pairs of prime numbers that differ by exactly 2 (such as 3 and 5, 11 and 13, 17 and 19, or 41 and 43).