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The paper investigates an approach to find out an objective integer in a large integer interval. It first puts forward an approach to subdivide a large integer interval into small ones that are available for the Monte Carlo randomized search algorithm, then selects a small interval by the Monte Carlo algorithm and applies a deterministic search algorithm on the selected one. In order to make the search in an expected computing time, the paper proposes certain regulations to set an initial length for the small interval and to update it in accordance with the expectation of the time complexity. Mathematical foundations for setting-up the initial value and updating it to an acceptable value are presented and proved in detail and a parallel computing strategy is introduced to realized it. Except for the availability in integer factorization, the approach is also applicable in big data searches.

Deterministic-Embedded Monte Carlo Approach to Find out an Objective Item in a Large Number of Data Sets