Mills showed that there exists a constant A such that ⌊ A³ⁿ ⌋ is prime for every positive integer n. Kuipers and Ansari generalized this result to ⌊ A^cn ⌋ where c ∈ R and c ≥ 2.106. The main contribution of this paper is a proof that the function ⌈ B^cn ⌉ is also a prime-representing function, where ⌈ X ⌉ denotes the ceiling or least integer function. Moreover, the first 10 primes in the sequence generated in the case c = 3 are calculated. Lastly, the value of B is approximated to the first 5500 digits and is shown to begin with 1.2405547052... .