## R, 38

    library(Rmpfr)
    round(rnorm(1,2e6,1e6))

Draws from the Gaussian distribution with mean 2,000,000, chosen randomly, and standard deviation 1,000,000, so that about 2/3 of the draws will lie within 1,000,000 and 3,000,000. The distribution is unbounded so in theory this can generate any integer. The Rmpfr package replaces R's built in double floats with arbitrary precision.