Fibonacci & Prime Tools
Check primality, Fibonacci membership, factorization & generate sequences
Prime?
✓ YES
Fibonacci?
✗ NO
Prime Factorization
Unique factors: 97 · GCD with itself: 97
About the Prime and Fibonacci Number Tools
These number tools test whether an integer is prime, break it into its prime factors, check whether it belongs to the Fibonacci sequence, and generate Fibonacci terms — all computed exactly in your browser.
A prime factorization calculator breaks an integer into the primes that multiply to make it — 360 becomes 2 × 2 × 2 × 3 × 3 × 5. That decomposition is unique for every integer above one, which is why so much of number theory and cryptography rests on it.
Primality is the related question, and the two are very different in difficulty. Deciding whether a number is prime is quick; finding the factors of a large one is not, and the whole of RSA depends on that asymmetry. Here both are done by trial division, which is exact and fast at the sizes this page accepts.
The Fibonacci side answers whether a number appears in the sequence, and generates terms on request. The terms are built by adding digit strings rather than using floating-point numbers, so the values stay exact well past the point where ordinary JavaScript arithmetic would start rounding.
How to use the Prime and Fibonacci Number Tools
- Enter a number. Type the integer you want to examine.
- Read the checks. See whether it is prime and whether it is a Fibonacci number.
- Read the factorisation. See the prime factors that multiply to make it.
- Or generate a sequence. Switch to the Fibonacci tab and choose how many terms you want.
Prime and Fibonacci Number Tools features
- Primality test for integers up to a billion
- Prime factorisation up to a hundred million
- Fibonacci membership by exact perfect-square test
- Fibonacci sequence generated to 80 terms
- Sequence terms computed exactly, without floating-point rounding
- Runs in your browser; nothing is uploaded
Frequently asked questions
What counts as a prime number?
An integer above 1 whose only divisors are 1 and itself. 1 is not prime by convention, and 2 is the only even prime — which is why every other prime is odd.
Why is there a size limit?
Because the answers are computed by trial division, which stays instant up to the limits shown and then starts to crawl. Rather than let the page hang on a huge input, results are offered only where they can be produced immediately.
Why does factorisation matter for cryptography?
Because multiplying two large primes is easy and recovering them from the product is not. RSA keys are built on exactly that gap, which is also why the numbers involved are hundreds of digits long rather than the sizes this page handles.
How is Fibonacci membership decided?
By the standard test: a number is a Fibonacci number precisely when 5n² + 4 or 5n² − 4 is a perfect square. That answers the question directly rather than generating the sequence up to your number first. Because it squares your input, the test is dependable up to around 40 million, above which 5n² outgrows the range where whole numbers stay exact.
Why do the sequence terms stay exact?
Because they are added as digit strings rather than as numbers. Ordinary JavaScript arithmetic loses precision above about nine quadrillion, which would silently corrupt the later terms.