Apparently, there is a formula for computing C as an infinite (limit) sum
but it is a kind  of a joke because involves the prime numbers,

Analytic formula for the nth prime. · Issue #181 · leios/SoME_Topics ·
GitHub <https://github.com/leios/SoME_Topics/issues/181>

You might also be interested in,

Formula for primes - Wikipedia
<https://en.wikipedia.org/wiki/Formula_for_primes>



On Fri, Jul 1, 2022 at 11:02 PM Raul Miller <[email protected]> wrote:

>    C=: 359344964622775339841352348439200241924659634x%10^45x
>    P=: {{ <. (0 2 4 p.y)*1|C*!_1 2 p.y }}@x:
>    P 1+i.18
> 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
>
> Sadly, this stops producing prime numbers for larger values of y.
>
> I'm told that there's a more exact value for C, where this expression
> would produce arbitrarily large prime numbers. But I don't know how to
> calculate a more accurate value for C.
>
> --
> Raul
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