This paper represents the preliminary results and conclusions on the one of fundamental questions of the genetic code related to the underlying selective mechanisms involved in its origin and evolution, in particular their hypothetical different nature, originally considered in [1,2,3]. A novel approach is introduced, based on known arithmetic regularities inside the genetic code, determined by the nucleon balances of amino acids and their divisibility by the decimal number 37 [4]. As a parameter of the genetic code systematization is introduced an aggregate nucleon number of amino acid and cognate codon, while divisibility test is carried out not only by the number 37, but also by 13.7, the selfsimilarity constant of decimal scaling [5]. Relevant nucleon sums were obtained for the most prominent divisions of the standard genetic code (SGC) according to p-adic model of the vertebrate mitochondrial code (VMC) in [6]. The nucleon number divisibility pattern of 37 and 13.7 for the RNA and DNA codon space, as well as for the amino acid space is also analyzed. The obtained results, particularly a general higher divisibility of the nucleon sums by the numbers 37 and 13.7 in SGC than in VMC, as well as a correspondence between the nucleon number divisibility pattern of both the RNA codon space and the amino acid space of SGC, how separately so conjointly, with the code degeneracy pattern, suggest some conclusions: support the hypothesis [1,2,3,7] that the selective driving forces acting during an emergence (an ancient phase) and an evolution (a modern phase) of the genetic code are different, imply the existence of an environmental-dependent stereochemical mechanism throughout the entire period of the genetic code emergence and support a mineral-mediated origin of the genetic code [7,8].