Convert PI to base 4. Does my unique human genome exist in the sequence of digits? The human genome consists of sequences of BASE Pairs A G C T
Convert the number PI to base 4. Does my unique human genome exist in the sequence of digits? 

A heuristic argument would go as follows: Assume your genome $G$ is a string of $n\gg1$ digits over $\{0,1,2,3\}$. Denote by $x_k$ the $k^{\rm th}$ digit of $\pi$ in base $4$. For each $r\geq0$ the probability  that
$$(x_{rn+1},x_{rn+2},\ldots,x_{rn+n-1}, x_{(r+1)n})\ne G$$
amounts to $(4^n-1)/ 4^n<1$. Therefore the probability that for no $r\geq0$ we have  a coincidence is
$$\lim_{N\to\infty}\left({4^n-1\over 4^n}\right)^N=0\ .$$
