TL;DR: Same result as stat_facts, but another way of explaining it. ;)
Discovery of blocks is a Poisson process.
The probability that
x blocks are found in the time that we expected
λ blocks to be found is:
Now, you have specified that you want to have six blocks found with a confidence of 99%.
The sum of probabilities of all possible outcomes always is 1. This means that we can express the probability of all outcomes where at least six blocks have been found as "100% minus the probability of having found less than six blocks".
p(x≥6|λ) = 1 - p(5|λ) - p(4|λ) - p(3|λ) - p(2|λ) - p(1|λ) - p(0|λ) = 0.99
x values into the above formula we get:
The resulting probability curve looks like this (y-axis is probability and x-axis is λ):
Finally, you were asking for
p(x≥6|λ) = 0.99 which turns out to be at about
λ ≈ 13.1085. Since the expected time for one block is 10 minutes, this means that in 131 minutes for 99% of the cases at least six blocks will have been found.