Clarify isprime documentation

[fingolfin]

Right now the docstring just says:

"""
    isprime(n::Integer) -> Bool

Returns `true` if `n` is prime, and `false` otherwise.

```julia
julia> isprime(3)
true

"""

But that's misleading because for large inputs, the result is only probabilistic.

Conversely, it *seems* to me that for $n < 2^{64}$ the test is proven to be accurate, i.e., deterministic. That would also be good to know and state explicitly.

I would provide a PR if that's desirable and if someone would confirm my guess above.

[oscardssmith]

That's a good point. You are correct that it is deterministic below 2^64 (modulo bugs) and is probabilistic above 2^64, but still safe enough for cryptographic purposes (assuming you don't need constant time guarantees). Specifically there are conjectured to be infinitely many cases where it falsely returns true, but they should be rare enough that finding one would require a fairly significant breakthrough in number theory.

[fepaul-book]

I updated the documentation and added a pull request
I looked at the code and made the same conclusions like you

For General Integer Types:
If the integer is within the range of a 64-bit integer, the Int64 implementation is used. Otherwise, the BigInt implementation is used.

For Int64 (64-bit integers):
The function first checks for even numbers and identifies 2 as the only even prime.
For numbers less than a certain small limit (N_SMALL_FACTORS), it uses a lookup table to quickly determine primality.
For larger numbers, the function uses a combination of trial division (to rule out small prime factors) and more advanced primality tests like the Miller-Rabin test and Lucas test. The Miller-Rabin test is an efficient probabilistic test for determining if a number is composite (not prime), and the Lucas test (deterministic) is used to further confirm the primality of the number.
Different bases and witnesses are chosen for the Miller-Rabin test based on the size of the number being tested.

For BigInt (arbitrarily large integers):
The function performs a probabilistic primality test with a configurable number of repetitions (reps). By default, it uses 25 repetitions, which is considered safe for cryptographic applications. This implementation uses the Miller-Rabin test with randomly chosen bases.