What is the Arabian Nights factorial, the number x such that x! has 1001 digits? How about the prime x such that x! has exactly 1001 zeroes on the tail end. (Bonus question, what is the 'rightmost' non-zero digit in x!?)

What is the Arabian Nights factorial, the number x such that x! has 1001 digits? How about the prime x such that x! has exactly 1001 zeroes on the tail end. (Bonus question, what is the 'rightmost' non-zero digit in x!?)

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