{"id":"integer-prime-factors","version":"1.0.0","description":"Compute the prime factorization of a positive integer as a list of prime/exponent pairs.","supported_operations":["integer prime factors","prime factorization","factorize integer"],"unsupported_operations":["factorization of 0 or negative integers","probabilistic factorization","divisor listing"],"semantics":["value is a canonical positive integer string from 1 to 1000000000000 (10^12) inclusive.","0 and negative values are rejected: prime factorization is only defined here for positive integers.","value 1 returns an empty factors array (the empty product).","factors is sorted ascending by prime, each entry { prime, exponent } with prime a canonical positive integer string and exponent a positive JSON integer.","Every listed prime, multiplied by itself exponent times across all entries, reconstructs value exactly.","Factorization uses exact trial division up to sqrt(value), bounded by the 10^12 input cap for predictable running time."],"limits":{"max_value":"1000000000000","max_digits":13},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["value"],"properties":{"value":{"type":"string","pattern":"^[1-9][0-9]*$","maxLength":13}}},"output_schema":{"type":"object","additionalProperties":false,"required":["factors"],"properties":{"factors":{"type":"array","items":{"type":"object","additionalProperties":false,"required":["prime","exponent"],"properties":{"prime":{"type":"string"},"exponent":{"type":"integer","minimum":1}}}}}},"examples":[{"input":{"value":"360"},"output":{"factors":[{"prime":"2","exponent":3},{"prime":"3","exponent":2},{"prime":"5","exponent":1}]}}],"execute_url":"/v1/tools/integer-prime-factors/versions/1.0.0/execute"}