Introduction:
In the RSA cryptosystem, the security of the encryption relies on the difficulty of factoring large prime numbers. The public and private keys are generated using two prime numbers, and the private key is kept secret while the public key is shared with others. In this scenario, participant A has chosen two prime numbers, P = 13 and Q = 17, to generate their keys.

Public Key Generation:
To generate the public key, participant A needs to calculate the modulus and the public exponent. The modulus (N) is calculated by multiplying the two prime numbers: N = P * Q = 13 * 17 = 221.

The public exponent (e) is typically a small prime number that is coprime with (P-1)*(Q-1). In this case, we are given that the public key is 35. So, the public exponent can be calculated by solving the equation: e * d ≡ 1 (mod (P-1)*(Q-1)). Since we know that e = 35, we can substitute the values and solve for d.

Private Key Generation:
The private key is calculated using the extended Euclidean algorithm. The algorithm finds the multiplicative inverse of the public exponent (e) modulo (P-1)*(Q-1). In this case, we need to find the value of d such that (35 * d) % ((13-1)*(17-1)) = 1.

So, by applying the extended Euclidean algorithm, we find that d = 59. Hence, the private key of participant A is 59.

Efficiency for Bigger Values:
The answer "Efficient for bigger values" indicates that the RSA cryptosystem is efficient for larger prime numbers. This is because factoring large prime numbers becomes increasingly difficult as the numbers get larger.

In this scenario, the prime numbers chosen by participant A are relatively small (P = 13 and Q = 17). While these numbers are sufficient for understanding the concept of RSA, they are not considered secure in practice.

In real-world applications, much larger prime numbers are used to generate the keys. These prime numbers can have hundreds or even thousands of digits. The larger the prime numbers, the more secure the RSA cryptosystem becomes, as factoring them becomes computationally infeasible.

So, while the given prime numbers P = 13 and Q = 17 are sufficient for demonstrating the concept of RSA, they are not considered secure. In practice, much larger prime numbers are used to ensure the confidentiality and integrity of the encrypted data.