ohoho, this is pernicious (following the wikipedia article on rsa, to the letter >:), mostly c):

struct KeyPair generate_RSA_keypair() {
    struct KeyPair keypair;
    bigint p = generate_prime();
    bigint q = generate_prime();
    bigint n = p*q;
    bigint totient = (p-1) * (q-1);
    bigint e = 1;
    while (gcd(e, totient) != 1) {
        e++;
    }
    bigint d = modular_inverse(e, totient);
    keypair.n = n;
    keypair.e = e;
    keypair.d = d;
    return keypair;
}