Many competitive programming problems involve prime numbers, and solving these efficiently requires using specialized algorithms. For generating prime numbers up to a certain limit, the Sieve of Eratosthenes is one of the most efficient algorithms with a time complexity of O(n log log n). It allows you to precompute prime numbers and use them for further operations. For problems involving prime factorization, the trial division method works for smaller numbers, but for larger inputs, algorithms like Pollard’s rho or optimized versions of trial division are faster. Using precomputed prime numbers and efficient algorithms helps in solving prime-related problems within time limits in competitive programming.