4372

4372 is an integer that is even and composite, situated between 4000 and 5000. In number theory, it serves as a simple example of a product of a small power of two and a larger prime.

Its prime factorization is 2^2 × 1093, where 1093 is a prime number. Consequently, the divisors of 4372 are 1, 2, 4, 1093, 2186, and 4372. The digit sum is 16, so the number is not divisible by 3, and it is divisible by 4 but not by 8. It is not a perfect square.

4372 can be expressed as a sum of two squares: 4372 = 66^2 + 4^2. This representation follows from the fact that 1093 = 33^2 + 2^2 and the identity (a^2 + b^2) × 4 = (2a)^2 + (2b)^2.

In base representations, 4372 equals 0x1114 in hexadecimal and 1000100010100 in binary. The Euler totient function value is φ(4372) = 2184.

From a number-theoretic perspective, 1093 is notable as a Wieferich prime to base 2, meaning 2^1092 ≡ 1 (mod 1093). This property is of interest in modular arithmetic and the study of rare primes.

Overall, 4372 serves as a concise example of a composite number with a small power of two and a large prime factor, illustrating how such numbers behave under factorization, modular properties, and representations in different bases.