Leetcode 2584. Split the Array to Make Coprime Products

Find the smallest index i where the product of nums[0..i] and nums[i+1..n-1] are coprime — equivalently, where no prime factor appears on both sides. With n up to 10^4 and nums[i] up to 10^6, the core challenge is efficient prime factorization and tracking counts of prime factors across the split to detect the earliest index with zero shared primes.