In mathematics, the weak conjecture is a statement in number theory that suggests that there are infinitely many prime numbers. The conjecture is named after the mathematician who first proposed it, Weakly.
The weak conjecture has been proven to be true for some specific cases, such as when n is a power of two. However, the general case remains unproven. If true, the weak conjecture would imply that the distribution of prime numbers is not random, as some mathematicians believe.
Weakly’s original formulation of the conjecture was as follows: “For every integer n > 1, there exists an infinite sequence of primes p_1,…,p_n such that p_1 < ... < p_n and p_n+1 > 2p_n.” In other words, Weakly conjectured that given any integer n greater than one, there are an infinite number of primes spaced at least n apart from each other.
The weak conjecture has been studied extensively since it was first proposed. Many mathematicians have attempted to prove or disprove the conjecture using a variety of methods. So far, all attempts have failed and the conjecture remains unproven.