Modern isogeny-based post quantum cryptographic schemes, like SQISign 1.0, including its variant AprèsSQI, rely on large primes p such that \(p^2 - 1\) is divisible by a large smooth factor. In order to find those, it is easiest to find smooth twins, consecutive smooth integers, that sum to a prime number. In this paper we develop novel methods to make an algorithm for finding smooth twins by solving Pell equations feasible to search for practical parameters for isogeny-based post quantum cryptography schemes. Our improvements here are twofold: First, we improve the runtime of the algorithm from exponential to polynomial and second, we introduce a way to enforce special requirements, that are necessary for practical applications. Our main method, which we call Pell-and-boost, is based on the infrastructure of orders in real quadratic number fields and a previous technique for finding smooth twins. While similar methods have been used in the past, they have never been powerful enough to compute parameters for practical use cases, we remedy this and showcase how our new techniques can compute potential candidates for primes.