The twin prime conjecture posits that there are an infinite number of twin primes.

sum_(n=1)^∞Boole(p_(n + 1) - p_n = 2) = ∞

Hilbert's eighth problem | Landau's second problem

formulation date | 1849 (176 years ago) formulator | Alphonse de Polignac status | open

sum_(n=1)^∞Boole(p_(n + 1) - p_n = 2) = ∞

The largest value known for the twin prime counting function is π_2(10^16) = 10304195697298.

mathematical conjectures | Landau's problems | unsolved mathematics problems