Twin Prime Checker
Check whether two numbers form a twin prime pair (both prime, difference of 2).
Inputs
First candidate of the twin prime pair.
Second candidate of the twin prime pair.
Twin Prime Pair?
Yes
First Number Prime?
Yes
Second Number Prime?
Yes
Difference
2
Step by step
Is 11 prime?
= Yes
Is 13 prime?
= Yes
Difference
= 2
Twin prime pair?
= Yes — (11, 13)
How it works
Twin primes are pairs of prime numbers that differ by exactly 2, such as (3, 5), (11, 13), and (17, 19). The Twin Prime Conjecture — that there are infinitely many such pairs — remains unproven. This calculator checks that both inputs are prime and that their absolute difference is 2.
Formula
Twin prime condition
(p, p+2) are twin primes ⟺ p is prime AND p+2 is prime
- p
- Smaller prime of the pair
Frequently Asked Questions
What are some examples of twin primes?
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).
Are there infinitely many twin primes?
This is the famous Twin Prime Conjecture. It has not been proven or disproven. In 2013, Yitang Zhang proved there are infinitely many pairs of primes with gap ≤ 70 million, later reduced to 246.