At least one prime less than n (n >= 2) is known to be used as a factor for composites between n and n^2, and this is explained by prime wave analysis. In this paper, the prime wave analysis is modified with a modular operator and applied to finding new primes within a limited boundary. In results, using the known primes less than 3, the composites were eliminated, and collected remaining prime candidates within a limited boundary between 3 and 3^2. The boundary was sequentially extended from 3^2 to 9^2, 81^2, and 6561^2 by finding 2, 18, 825, and 2606318 prime candidates; these candidates were verified as new primes using the using online databases. In addition, the boundary was extended from 6561^2 to 43046721^2 and the serial new primes were also found within a randomly selected boundary between 6561^2 and 43046721^2. In general, it was concluded that the prime wave analysis modified with a modular operator could be a practical technique for finding new primes within a limited boundary.