Boolean function minimization is an area important not only in the development and optimization of digital logic, but also in other research and development areas, such as, the optimization of control systems, simplifying program logic, artificial intelligence, etc. The aim of this paper is to present a hardware accelerated first step of the systematic minimization of single-output Boolean functionsthe generation of a set of prime implicants for both the disjunctive normal form (DNF) and the conjunctive normal form (CNF), having defined the OFF and ON sets andalternativelyalso the DC ("don't care") set. The proposed hardware accelerator is designed as combinational logic, described in VHDL. Its advantages include an extremely short prime-implicant-generation time in the order of ns and/or tens of nsin case of Boolean functions with small amount of input variablesand the possibility to generate the valid-prime-implicant set of Boolean functions having a defined number of input variables at a constant time, regardless of the cardinality of the ON or, eventually, the DC sets. However, these advantages come with a large spatial complexitythe number of utilized implementation elementsof the respective combinational module, generating the prime-implicant set. The authors verified the proposed design using Field Programmable Gate Array (FPGA) technology, implementing the hardware using a Xilinx Kintex-7 KC-705 Evaluation Kit development board.