a(n) = prime((n+1)!) - prime(n!).

Terms

a(0) =1a(1) =10a(2) =76a(3) =570a(4) =4784a(5) =43590a(6) =435004a(7) =4738392a(8) =55972218a(9) =713630736a(10) =9777359856a(11) =143350864898