The straight line complexity of small factorials and primorials

In this paper we determine the straight-line complexity of $n!$ for $n\leq 22$ and give bounds for the complexities up to $n=46$. In the same way we determine the straight-line complexity of the product of the first primes up to $p=31$ and gives bounds for $p\leq 43$. Our results are based on an exhaustive computer search of the short length straight-line programs.

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