Existing CAS commands --> Prime discussion

[parisse]

isprime on the Prime returns 1 if the number is pseudoprime, it is not a proof of primality (except for "small" numbers) and there is nothing on the Prime to return a certificate of primality.

About roots: most of the time, proot will return accurate roots, but it may fail for very specific polynomials that have two roots almost identical (and zeros will almost never be able to return exact roots).
Classical example is Mignotte polynomial
mig(n,t):=x^n-((2^(t/2)-1)*x-1)^2
For example mig(257,14)==x^257-(127*x-1)^2 has two roots near 1/127.
realroot finds these roots with precision 1e-15 in about 0.03s on my computer, proot requires more than 6s (of course it also computes complex roots).