Factorial creates Prime

Number Theory Level pending

There is a number \(N>2\) such that the digits of \(N!\) can be rearranged to form a prime.

Now, which of the following option is correct?

\(A :\) There exists infinitely many numbers \(N\).
\(B :\) There exist only one such number \(N\).
\(C :\) All prime numbers greater than \(2\) satisfy the conditions of \(N\).
\(D :\) There is no number satisfying the condition of \(N\)


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