Prime Number Checker

Prime Number Checker — The Fastest Way to Test Any Integer

Our prime number checker is a free is it prime calculator that tests any positive integer in milliseconds. Whether you need to check if a number is prime, factor a composite, or generate prime numbers between two numbers, this prime calculator does it all in your browser with zero uploads. Type a number above — or open a shareable link such as ?n=1000000007 — and the prime detector returns an instant verdict with execution time, full prime factorization, and a complete divisor list.

What Is a Prime Number?

A prime number is a natural number greater than 1 that has exactly two positive divisors: 1 and itself. In other words, a prime cannot be formed by multiplying two smaller natural numbers. The first few primes are 2, 3, 5, 7, 11, and 13. Any number greater than 1 that is not prime is called a composite number — for example, 6 is composite because it can be divided by 1, 2, 3, and 6.

Two common questions get asked constantly. Is 1 a prime number? No — a prime must have exactly two distinct divisors, and 1 has only one, so it is a unit. Is 0 a prime number? No — 0 is divisible by every integer, which is why our is 0 a prime number calculator reports it as neither prime nor composite. And 2 is the only even prime number; every other even integer is divisible by 2.

The Fundamental Theorem of Arithmetic states that every integer greater than 1 has a unique prime factorization. For example, 60 = 2² × 3 × 5. This uniqueness is what makes primes the fundamental building blocks of all integers and the bedrock of number theory, cryptography, and computer science.

How to Check If a Large Number Is Prime Online

Checking large numbers by hand is impractical, and most calculators fail past 15 digits. Here is how this online primality test handles every size of input:

• Small inputs (< 2⁵³): instant optimized trial division testing only divisors of the form 6k ± 1 up to √n — skipping evens and multiples of 3.
• Large inputs (up to 1000 digits): the deterministic Miller-Rabin primality test. Below 3.3 × 10²⁴ the twelve bases 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 prove primality with certainty; larger values use 32 randomized rounds with error probability under 2⁻⁶⁴.
• Non-blocking Web Worker: every heavy calculation runs on a background thread using native BigInt arithmetic, so the page never freezes and the execution time is shown in milliseconds.

This makes it one of the fastest online Miller-Rabin primality tests available — try a 100+ digit number and watch the verdict return instantly.

Prime Factorization Tool & Factor Tree Generator With Steps

Beyond primality, this prime factor calculator produces the complete factorization of any composite using trial division plus Pollard's Rho for large cofactors. Results use exponent notation (e.g., 360 = 2³ × 3² × 5), include the factor count, and list every divisor. For visualization, the prime factor tree generator with steps draws an interactive SVG tree that shows each split — like 60 → 2 × 30 → 2 × 2 × 15 → 2 × 2 × 3 × 5 — alongside the numerical steps.

Prime Number Generator Between Two Numbers

The built-in prime number generator lists every prime between any two bounds using the Sieve of Eratosthenes — the classic algorithm that marks multiples of each prime up to √B and collects the survivors. The output shows the total count, the execution time, and the full list, which you can copy or download as CSV, plain text, or JSON. Generate the 25 primes from 1 to 100, or find every prime number between 100 and 1000 in one click.

Find the Next Prime Number After X

Need to find the next prime number after X? Enter any value and press "Find nearest primes" to get both the next prime above it and the previous prime below it, including the gap between them. The search uses Miller-Rabin screening so it returns instantly even for gigantic starting values.

Special Prime Classifier: Twin, Mersenne & More

The special prime classifier automatically detects rare categories so you can check twin primes and Mersenne primes online without knowing the math:

• Twin Prime: the number and a neighbor differ by exactly 2, e.g. (11, 13).
• Mersenne Prime: of the form 2^p − 1 with p prime, e.g. 7, 31, 127.
• Fermat Prime: of the form 2^(2^k) + 1, e.g. 5, 17, 257.
• Fibonacci Prime: a prime appearing in the Fibonacci sequence, e.g. 13, 89.
• Palindromic Prime: reads the same forwards and backwards, e.g. 929.

Batch Primality Checker

The batch primality checker accepts a list of numbers separated by commas, spaces, or new lines (up to 200 at once) and checks them simultaneously. Results appear in a table with each number's status — prime, composite, unit, or invalid — plus its prime factorization, exportable as CSV. Perfect for homework sets, coding puzzles, or validating sequences.

Prime Numbers from 1 to 100

There are exactly 25 prime numbers between 1 and 100:

Notable observations: 2 is the only even prime. The pair (3, 5) is the smallest set of twin primes. Whether infinitely many twin primes exist remains an open question known as the Twin Prime Conjecture, one of mathematics' most famous unsolved problems.

Why Prime Numbers Matter

Primes are the foundation of modern cryptography. RSA encryption multiplies two huge primes together; breaking the cipher requires factoring the product back into them, which is computationally infeasible for numbers with hundreds of digits. Every HTTPS connection, digital signature, and blockchain transaction depends on this asymmetry. The Prime Number Theorem — stating that primes near N occur roughly every ln(N) integers — remains central to research into the distribution of primes and the Riemann Hypothesis.