The global analysis of 3 human genomes of increasing levels of evolution (neanderthal / sapiens build34 of 2003 / sapiens hg38 of 2013) reveals 2 levels of numerical constraints controlling, structuring and optimizing the DNA sequences of these genomes. A global constraint - which we will call "HGO" for "Human Genome Optimum" - optimizes the genome at its global scale of 3.5 billion base pairs. This same operator when applied to each of the 24 individual chromosomes reveals a hierarchical structure of these 24 chromosomes according to a numerical spectrum of amplitude ½ Phi extending from chromosome 4 to chromosome 19. This first level of comparison reveals a very Great analogy between these 3 genomes. Then we introduce a global analysis method of roughness or fractal texture of the DNA sequences at the level of each chromosome. After having demonstrated that the chromosome4 seems to play a privileged role in the human genome, radically differentiating it from the 23 other chromosomes, we limit the study to the exhaustive analysis of different whole chromosomes4 relative to the 6 primates Homosapiens, Neanderthal, Chimpanzee, Orang-outan, Gorilla and Macaque. There are then remarkable resonances and periods - based on the sequences of Fibonacci and Lucas - totally differentiating the chromosomes 4 of these different primate species: 21 base pairs period for the chimpanzee and the urang-outan, 34 bases pairs period for Man, and 55 base pairs period for the gorilla. Finally, the major result is that the comparative analysis of the respective chromosomes4 of sapiens and neanderthal shows for the first time major differences in long-range fractal structures between the DNA sequences of these two genomes. Thus, while the chromosome4 of sapiens has an obvious resonance of 34 nucleotides, that of Neanderthal seems "torn" between two attractors of fractal textures, one on this same resonance 34, but with a roughness radically different from that of sapiens, While the other resonance is tuned to the number of Lucas 123. Finally, on a more theoretical level, this method reveals properties of "discrete digital standing waves" such as periods, resonances, phase shifts or phase positions. To conclude, we suggest that this chromosome4 could possibly play a role as a "referential" with respect to each of the 23 other chromosomes of the nuclear genome and possibly also with respect to the mitochondrial mtDNA genome. Show less