You might want to take it one step further and add the prime multiplication to non-prime tables to your repertoire of facts. There are only 168 primes to 1000, quick recognition that these cannot be factored and practiced facility with calculating with them could add a some pleasant improvements. On the other hand it might just be a fun project with no positive outcomes other than an increased sense of numeracy. As an adult I find that trying to wire up numeracy takes time and repetition so a project like this would probably reap the additional benefits of practice and time while it kept me motivated.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997

In daily use all I come up with is that quickly recognizing that a number cannot be decomposed keeps you from wasting time down an unfruitful path. Factorization is a practical element. From a numerical perspective they are fascinating. If you think of it one way all natural numbers are composed of primes. Mathematicians have spent life times trying to understand their nature and for the most part failing. Ulam Spirals mess with my head. https://www.youtube.com/watch?v=iFuR97YcSLM.