The binomial coefficient $\displaystyle{\binom{10^{18}}{10^9}}$ is a number with more than $9$ billion ($9\times 10^9$) digits.
Let $M(n,k,m)$ denote the binomial coefficient $\displaystyle{\binom{n}{k}}$ modulo $m$.
Calculate $\displaystyle{\sum M(10^{18},10^9,p\cdot q\cdot r)}$ for $1000\lt p\lt q\lt r\lt 5000$ and $p$,$q$,$r$ prime.
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