Polignac's_equation
Polignac's equation is a mathematical equation in number theory that states that for any even integer n, there are infinitely many prime numbers p such that p + n is also a prime. This equation is named after the French mathematician Alphonse de Polignac, who first proposed the conjecture in 1849. The equation is a generalization of the twin prime conjecture, which is the case when n = 2. Despite extensive research, the conjecture remains unproven, but significant progress has been made in recent years, including the work of Yitang Zhang and the Polymath project, which have shown that there are infinitely many prime pairs with a bounded gap. The equation has important implications for the distribution of prime numbers and has connections to other areas of mathematics, such as sieve theory and analytic number theory.
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