twin prime conjecture

《Algebraic Number Theory》 · 第 103 页 · Section 3.5「Notes」，§3.4

The twin prime conjecture is a special case of the prime $k$-tuple conjecture. The prime $k$-tuple conjecture asserts that if $b(p)<p$ for every prime number $p$, then there exist infinitely many positive integers $n$ such that the $k$ numbers $n+d_i$ are all prime.

《Introduction to Analytic Number Theory》 · 第 6 页 · 导论「Prime Numbers」

Such pairs of primes which differ only by $2$ are known as twin primes. Many mathematicians think there are infinitely many such pairs, but no one has been able to prove this as yet.