nt.number theory – Certification of balanced prime, semi-prime, and semi-prime without totient


We can detect primes in polynomial time. Before that we had a Certificate of Primality by Pratt's Certificate.

To certify an integer $ N = PQ $ to be semi-prime we can provide the factors $ P $ Y $ Q $ and we can prove that they are cousins ​​and prove $ N = PQ $ sustains.

There cannot be a certificate similar to Pratt's certificate as that would require knowledge of $ phi (N) $ which is equivalent to factoring.

  1. Is there a different primality test with no properties of $ phi (N) = N-1 $ when $ N $ is he a cousin

  2. Is there a different certificate for semiprimes?

  3. What if we only consider balanced semiprimes where $ P $ Y $ Q $ have equal bit length?