q×p

q×p denotes the product of two integers q and p. In mathematical contexts, p and q are often primes, in which case the product is called a semiprime. If p and q are distinct primes, n = pq has exactly four positive divisors: 1, p, q, and pq. If p equals q, the product is p^2 and has divisors 1, p, p^2.

When p and q are primes, Euler's totient function satisfies φ(n) = (p−1)(q−1) for distinct primes, and φ(n) = p(p−1) if p = q. The number n is composite and its prime factorization is n = pq (with p and q being the prime factors). If p and q are distinct odd primes, n is odd and greater than p and q.

In cryptography, RSA-type systems use a modulus n = pq where p and q are large distinct primes. The security of such systems relies on the difficulty of factoring n back into p and q. Proper selection and secrecy of p and q, along with sufficiently large primes, are essential to resist factorization attacks.

In mathematics and computer science, the concept of pq appears in modular arithmetic, the Chinese remainder theorem, and primality testing. The product is commutative (pq = qp), and p and q are often treated as interchangeable in theoretical discussions. A simple example is p = 3 and q = 11, giving n = 33, whose divisors are 1, 3, 11, and 33.