Background/Objectives: The ~1.6 kb NBPF repeat units in neuroblastoma breakpoint family (NBPF) genes are specific to humans and are associated with cognitive capacity in higher primates. While the number of NBPF monomers/Olduvai sequences in humans is approximately 2–3 times greater than in great apes, the difference in copy number values of canonical NBPF 3mer Higher-order repeats (HORs)/Olduvai triplets between humans and great apes is substantially larger. This study aims to analyze the organization and evolutionary significance of NBPF 3mer HORs/Olduvai triplets in fully sequenced primate genomes. Methods: We applied the global repeat map (GRM) algorithm to identify canonical and variant NBPF 3mer HORs/Olduvai triplets in the complete genomes of humans, chimpanzees, gorillas, and orangutans. The resulting monomer arrays were analyzed using the GRMhor algorithm to generate detailed schematic representations of NBPF HOR organization. Results: The analysis reveals a distinct difference in NBPF-related patterns among these primates, particularly in the number of tandemly organized canonical 3mer HORs/Olduvai triplets: 61 tandemly organized canonical NBPF 3mer HORs/Olduvai triplets in humans, compared to 0 in chimpanzees and orangutans, and 9 in gorillas. When considering only tandemly organized 3mer HORs/Olduvai triplets with more than three copies, the numbers adjust to 36 in humans and 0 in great apes. Furthermore, the divergence between individual NBPF monomers in humans and great apes is twice as high as that observed within great apes. Conclusions: These findings support the hypothesis that the tandem organization of NBPF 3mer HORs/Olduvai triplets plays a crucial role in enhancing cognitive capacity in humans compared to great apes, potentially providing a significant evolutionary advantage. This effect complements the impact of the increased number of individual NBPF monomers/Olduvai sequences, together contributing to a synergistic amplification effect.