The scope of the work described in this paper is a systematic investigation as to whether or not the mass of the proton and the electron can be represented by other fundamental constants. The author arrives at the conclusion that the mass of the proton and the electron can be expressed by a combination of five constants that occur in nature; namely, e, εo, h, c, G, plus a time-variable parameter. In this context, the author has studied more than 37,000 options using electronic support and powering the fundamental constants with natural numbers only. The simplest and most convincing formula the author has found is: me3 x mp3 = (e2 h/4p εo c G R)2 This equation results in the exact value of the mass of the proton and the electron. The beauty and simplicity of this equation give rise to the following question: What, if not this formula, is able to represent the mass of the two most important particles? The author’s conclusion is that either the electron and proton masses themselves are natural constants that cannot be represented by other constants of nature, or that – as shown in this paper – they can be perfectly well represented by five other fundamental constants, in addition to a time-variable parameter.