So, been trying to figure out how to do something, and researching it online, and came across the term "Primorial(s)"... Meaning the Product of the first n Prime Numbers. (Say, multiplying the first n=10 Prime Numbers together, etc.)

https://en.wikipedia.org/wiki/Primorial

Is there a function in Mathematica for this? I'm having a tough time finding one. Seems fairly basic. Like I'm pretty sure there's a function to list the n-th Prime number. Yep:

https://reference.wolfram.com/language/ref/Prime.html

So, one would think it would be simple to implement a Function that multiplies the first n such primes together, and call that function "Primorial [n]," or whatever?

I see an entry on Math World:

https://mathworld.wolfram.com/Primorial.html

But, I'm having a hard time locating an actual Mathematica function for it? Is there one?

If not, could Wolfram please create one and add it perhaps to the next iterative .x release of Mathematica? For those of us interested in Prime #'s, Prime Theory, Prime Sieving, and such.

There's actually a fairly real-world usage case for it in Sieving. Would be handy to have a simple function for it. Where you could just be like Primorial[10]; and have it return the answer... Which looks to be around ... jeez, even Wolfram|Alpha can't parse my input "Product of the first 10 prime numbers." It'll do "Sum" fine. Sigh Okay, doing it manually... Around ... 6,469,693,230

So, yeah, it'd be nice if one had a simple function to input:

Primorial[10];

and get output:

6,469,693,230

Yeah?

Does this exist, or can it be added?

If it doesn't exist? How can it be done in Mathematica? Can one do like a table / array or something and the take the product of all of it?

And then, for the thing I kind of want to do, count the digits of the result with "IntegerLength[]"?

https://reference.wolfram.com/language/ref/IntegerLength.html