I am carrying out my research for optimized software, and all the papers I find on the subject.

I hope to find who is serious enough to look at the content and substance and not at the mere form of message.

So here's the Paper link from ResearchGate

https://www.researchgate.net/publica...ble_Prime_Test
This possibility to make a program that can compute both Mersenne and Fermat numbers.

Abstract

Based on the well-known Baillie/Wagstaff suggestion [R. Baillie and S. Wagstaff jun., Math. Comput. 35, 1391-1417 (1980; Zbl 0458.10003)] we introduce a rapid pseudoprimality test with high confidence. The test is extremely fast and only requires evaluation of power polynomials and the Lucas V-sequence. This is in contrast to the original version, where usually the more cumbersome evaluation of the Lucas U-sequence is required as well. We analyze the underlying properties of the proposed test and give a characterization of the pseudoprimes. Software and hardware evaluation methods for both modular exponentiation and evaluation of recursion sequences are widely employed and very efficient. Therefore the test can be run at low cost for varieties of different bases/parameters. The number of those that pass the test are of great interest. We exhibit the exact number of these “liars”.