Prime Number Checker
Check whether any integer is a prime or composite number.
Prime Number Checker & Factorization
About Prime Number Checker
The Prime Number Checker & Primality Test Calculator tests whether any positive integer is Prime or Composite using Miller-Rabin probabilistic tests, deterministic trial division, finding the nearest preceding and next prime numbers.
How to Use Prime Number Checker
Step 1
Enter any positive integer.
Step 2
Click "Check Primality".
Step 3
Inspect the Prime/Composite verdict badge, factor details, and adjacent primes.
Step 4
Click "Copy Report".
Practical Use Cases for Prime Number Checker
Mathematics Homework & Education
Verify primality for any number with full divisor lists and step-by-step division checks.
Cryptography & Hash Table Sizing
Find optimal prime numbers near specific array capacities to minimize hash collision clustering in hash tables.
Input & Output Examples
Checking Primality of 1,000,003
Number: 1000003
Status: Composite | Smallest Divisor: 7 (Factorization: 7 * 142857) | Nearest Primes: 999983 (Previous) and 1000033 (Next)
Key Features & Performance
- ✓Deterministic Miller-Rabin test for numbers up to $2^{64}$ and arbitrary-precision BigInt support.
- ✓Finds smallest prime factor and complete divisor list for composite numbers.
- ✓Locates Nearest Preceding Prime and Nearest Next Prime numbers.
- ✓100% Client-Side calculation.
- ✓1-Click Copy primality report.
Key Terminology & Definitions
Prime Number
A natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers (divisible only by 1 and itself).
Miller-Rabin Primality Test
A probabilistic primality test that determines whether a given number is composite or probable prime in $O(k \\log^3 n)$ polynomial time.