Most advantageous program written for 41/42?

[Allen]

I would tend to agree regarding the primality testing.

Many primality testing algorithms are quite fast if you have a modular exponentation function available on the calculator.

The Rabin-miller test for example can guarantee primailty for n < 1,122,004,669,633, by only testing 4 situations where a = 2, 13, 23, and 1662803. ( other bounds in the wikipedia article)

I heavily use a pollard-rho factorization algorithm on my 42s (excellent free42 emulator) which can factor any number my emulated 42s can handle in less than a second.