Is $a=\frac{1992!-1}{3449\times 8627}$ a prime number?

Question

Is $a=\dfrac{1992!-1}{3449\times 8627}$ a prime number ?
This is a natural follow-up to that recent MSE question

We know that $a$ has $5702$ digits and no prime divisor $<10^6$.

Answer 1

No, $\dfrac{1992!-1}{3449\times 8627}$ is divisible by $86544733151681393$, found using GMP-ECM.

Moreover, $\dfrac{1992!-1}{3449 \times 8627 \times 86544733151681393}$ is also not prime; it fails the Fermat Test for bases $a \in \{2,3,5,7\}$, checked with OpenPFGW.

Answer 2

I just ran a Rabin-Miller test on that number and I got the result "False" (i.e. it is NOT a prime number). If you want to know the divisors in addition to what you asked then I don't think that is computationally easy.

>>> rabinmiller(a,1)
False

Answer 3

Maple also says no:

is((factorial(1992)-1)/(3449*8627), prime);

$$\it{false}$$