Prime Number Checker
Check if any number is prime, decompose composite integers into prime factors, list every divisor, and find neighboring primes.
Fast deterministic Miller-Rabin test supports values up to 2⁵³ - 1 (9,007,199,254,740,991).
180 is a composite number divisible by 2.
All Positive Divisors (18 total)
Prime Numbers & The Fundamental Theorem of Arithmetic
The Fundamental Theorem of Arithmetic
Every positive integer greater than 1 can be represented uniquely as a product of prime powers, up to the order of the factors.
For example, 180 = 2² × 3² × 5. Prime numbers are the fundamental multiplicative building blocks of all integers.
Deterministic Miller-Rabin Primality Test
Simple trial division testing up to √n becomes too slow for 16-digit integers.
The deterministic Miller-Rabin test checks modular square roots of 1 using Fermat's Little Theorem bases: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37], guaranteeing 100% accuracy for all 64-bit integers.
Divisor Counting Formula τ(n)
If a number factors into p₁^a × p₂^b × p₃^c, the total number of positive divisors is:
For 180 (2² × 3² × 5¹): (2+1)(2+1)(1+1) = 3 × 3 × 2 = 18 divisors.