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Prime Number Checker

Check if a number is prime, find prime factors, and list primes in a range

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What is Prime Number Checker?

Free prime number checker. Check if any number is prime, find all prime factors, and list primes in any range. Instant results. Fast, accurate mathematical calculators that show step-by-step working. TekPulse's Prime Number Checker is completely free — no signup, no ads in results, and no data stored on our servers.

How to Use Prime Number Checker Online

  1. Enter any whole number in the input field
  2. Click Check — the tool immediately tells you whether the number is prime or composite
  3. For composite numbers, all prime factors are listed (prime factorization)
  4. Use the prime range finder to list all prime numbers up to a given limit
  5. Very large numbers (10+ digits) may take a moment to process using Miller-Rabin primality testing

Prime Number Checker Formula & Calculation

Trial division up to √n, checking only divisors of the form 6k±1

A number n is prime if it has no divisors other than 1 and itself. After quickly handling n < 2 (not prime), n < 4 (prime), and even numbers or multiples of 3, the checker only needs to test potential divisors up to √n — because if n has a factor larger than √n, it must also have a corresponding factor smaller than √n. All primes greater than 3 are of the form 6k±1, so only those candidates are tested, roughly tripling the speed versus checking every integer.

Example: Check 97 → √97 ≈ 9.85, so test divisors up to 9 using the 6k±1 pattern: 5, 7 → 97 is not divisible by either → 97 is prime.

Key Factors That Affect Your Result

  1. Why √n is sufficient — Testing divisors only up to the square root is mathematically sufficient and is what keeps this check fast even for numbers with several million as input, instead of testing every integer up to n.
  2. Factor listing — The "Find Factors" mode lists all divisors by checking up to √n and pairing each divisor i with n÷i, which is more efficient than checking every number from 1 to n.
  3. List primes in range — Generating a list of primes within a range re-runs the same trial-division check for each number in that range, so very large ranges will take proportionally longer.

Why Use TekPulse Prime Number Checker?

Runs Entirely in Your Browser
Primality checks and factorizations are computed instantly with JavaScript — nothing is uploaded
Trial Division Primality Test
Checks primality using an optimized trial-division algorithm and also finds the nearest next/previous prime
Prime Factorization
Breaks any number down into its prime factors and lists all divisors, including a perfect-number check
List Primes in a Range
Generates every prime number between two values up to 100,000

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Frequently Asked Questions

A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13. The number 1 is not prime. 2 is the only even prime.

Check if the number is divisible by any integer from 2 to √n. If no divisor is found, the number is prime. Example: Is 97 prime? √97 ≈ 9.8. Check 2,3,5,7 — none divide 97 evenly, so 97 is prime.

Twin primes are pairs of prime numbers that differ by 2: (3,5), (5,7), (11,13), (17,19), (29,31). Whether there are infinitely many twin primes is an unsolved mathematical problem (Twin Prime Conjecture).

Prime factorization expresses a number as a product of prime numbers. Example: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5. Every positive integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).

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