Problem 46054. Count trailing zeros in a primorial

Cody Problem 44068 asked us to count the trailing zeros in a factorial. This problem deals with the primorial. If p_n is the nth prime number, then the primorial p_n# is the product of the prime numbers up to and including p_n. For example, if n = 5, then p_5# = 2*3*5*7*11 = 2310, which has one trailing zero.
Count the trailing zeros in the primorial p_n#. Because primorials become large quickly, for large n it helps to derive a formula for the number of trailing zeros.*
Please make your code general because I might add more tests later.
*;-)
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Solution Stats

79.55% Correct | 20.45% Incorrect
Last Solution submitted on Oct 19, 2025

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