The program to use to prove a number prime depends entirely on the prime and your goal. If you just want any large prime n, then choose a form for which the classical tests apply (a for for which either n+1 or n-1 factors, see The Classical Tests. Proth.exe, PrimeForm, pfgw and prp are popular examples of programs to use for these numbers and are often preceeded by the use of a screening program such as NewPGen. Using the classical tests numbers with tens of thousands of digits may be easily proven prime.
If instead you already have your number and know very few factors of n2-1 (e.g., primes
from certain sequences, cryptographic primes...) then you must use a general test (see The general purpose tests. These tests are far slower than the classical test (because of the lack of special form) but are improving rapidly. The current record holder here is Titanix, followed by ECPP. APRT-CLE in UBASIC is nice for smaller numbers. There is also CYCLOPROVE and ...
It is not possible to give a general answer to what is the best program because it depends on too many factors! You might consider asking around (e.g. on the Primes Numbers mailing list).