The Riemann hypothesis is true up to 3·1012

We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height 3 · 10 12 . That is, all zeroes β + i γ of the Riemann zeta-function with 0 < γ ⩽ 3 · 10 12 have β = 1 / 2 . Moreover, all of these zeroes are simple.