Analyze Prime Numbers

Analyze prime numbers by selecting and applying the appropriate algorithm for the task at hand: primality testing, integer factorization, or prime distribution analysis. Verify results computationally and relate findings to the Prime Number Theorem.

When to Use

• Determining whether a given integer is prime or composite
• Finding the complete prime factorization of an integer
• Counting or listing primes up to a given bound
• Verifying the Prime Number Theorem approximation for a specific range
• Investigating properties of primes in a number-theoretic proof or computation

Inputs

• Required: The integer(s) to analyze, or a bound for distribution analysis
• Required: Task type -- one of: primality test, factorization, or distribution analysis
• Optional: Preferred algorithm (trial division, Miller-Rabin, Sieve of Eratosthenes, Pollard's rho)
• Optional: Whether to produce a formal proof of primality or just a computational verdict
• Optional: Output format (factor tree, prime list, count, table)