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Problem statement: Ffrequent patterns are patterns that appear in a data set frequently. Finding such frequent patterns plays an essential role in mining associations, correlations and many other interesting relationships among data. Approach: Most of the previous studies adopt an Apriorilike approach. For huge database it may need to generate a huge number of candidate sets. An interest solution is to design an approach that without generating candidate is able to mine frequent patterns. Results: An interesting method to frequent pattern mining without generating candidate pattern is called frequent-pattern growth, or simply FP-growth, which adopts a divide-and-conquer strategy as follows. However, for a large database, constructing a large tree in the memory is a time consuming task and increase the time of execution. In this study we introduce an algorithm to generate frequent patterns without generating a tree and therefore improve the time complexity and memory complexity as well. Our algorithm works based on prime factorization and is called Prime Factor Miner (PFM). Conclusion/Recommendations: This algorithm is able to achieve low memory order at O(1) which is significantly better than FP-growth

Using Unique-Prime-Factorization Theorem to Mine Frequent Patterns without Generating Tree