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# Factorials

2! = 2, 3! = 3*2, 4! = 4*3*2… and 100! is a lot better than writing out 158 digits. 90! is the largest factorial that can fit in a tweet.

# Factorials: Level 3 Challenges

How many of the following 99 integers are primes?

$\begin{array} &100!+2, &100!+3, &100!+4, &\ldots, &100!+100\end{array}$

How many positive integers are divisors of $$21!$$ but are not divisors of $$20!$$?

Find the remainder when $$70!$$ is divided by $$5183$$.

Note: Don't use a computational device!

$\large \lim_{n \rightarrow \infty} { 2n \choose n } ^ { \frac{1}{n} } = \ ?$

How many trailing zeroes are in the decimal representation of $n=1+\displaystyle{\sum_{k=1}^{2013}k!(k^3+2k^2+3k+1)}?$

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