Haskell, 91 bytes
import Data.Numbers.Primes
x=product[p^length[';'product[p^length[';'..c]|(c,p)<-zip"hNC@<=;;;;;:;:;:;::;"primes]
Try it online! (has an extra 2 bytes for x=
)
Probably suboptimal but I had a lot of fun writing it. I encode the prime exponents (including zeroes for the primes it doesn't have prior to 71) as a string using the character's relative distance from :
. the rest is a simple matter of zipping the exponents against an infinite list of all primes, raising those primes to that power, and taking the product.
Edit: forgot to take the x=
out of the source code on here.