Since ancient times aging has also been regarded as a disease, and humankind has always strived to extend the natural lifespan. Analyzing the genes involved in aging and disease allows for finding important indicators and biological markers for pathologies and possible therapeutic targets. An example of the use of omics technologies is the research regarding aging and the rare and fatal premature aging syndrome progeria (Hutchinson-Gilford progeria syndrome, HGPS). In our study, we focused on the in silico analysis of differentially expressed genes (DEGs) in progeria and aging, using a publicly available RNA-Seq dataset (GEO dataset GSE113957) and a variety of bioinformatics tools. Despite the GSE113957 RNA-Seq dataset being well-known and frequently analyzed, the RNA-Seq data shared by Fleischer et al. is far from exhausted and reusing and repurposing the data still reveals new insights. By analyzing the literature citing the use of the dataset and subsequently conducting a comparative analysis comparing the RNA-Seq data analyses of different subsets of the dataset (healthy children, nonagenarians and progeria patients), we identified several genes involved in both natural aging and progeria (KRT8, KRT18, ACKR4, CCL2, UCP2, ADAMTS15, ACTN4P1, WNT16, IGFBP2). Further analyzing these genes and the pathways involved indicated their possible roles in aging, suggesting the need for further in vitro and in vivo research. In this paper, we (1) compare “normal aging” (nonagenarians vs. healthy children) and progeria (HGPS patients vs. healthy children), (2) enlist genes possibly involved in both the natural aging process and progeria, including the first mention of IGFBP2 in progeria, (3) predict miRNAs and interactomes for WNT16 (hsa-mir-181a-5p), UCP2 (hsa-mir-26a-5p and hsa-mir-124-3p), and IGFBP2 (hsa-mir-124-3p, hsa-mir-126-3p, and hsa-mir-27b-3p), (4) demonstrate the compatibility of well-established R packages for RNA-Seq analysis for researchers interested but not yet familiar with this kind of analysis, and (5) present comparative proteomics analyses to show an association between our RNA-Seq data analyses and corresponding changes in protein expression.