Twin prime

Twin primes are pairs of prime numbers of the form $p$ and $p+2$. The first few pairs of twin primes are $(3, 5), (5, 7), (11, 13), (17, 19), (29, 31)$, and so on. Just as with the primes themselves, twin primes become more and more sparse as one looks at larger and larger numbers.

Twin Prime Conjecture

Main article: Twin Prime Conjecture

The Twin Prime Conjecture asserts that there are infinitely many pairs of twin primes. It is not known whether this statement is true.

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