This study aimed to identify candidate biomarkers for papillary thyroid carcinoma using an integrative analysis of bioinformatics and machine learning (ML). The PTC datasets GSE6004, GSE3467, and GSE33630 (species: Homo sapiens) were downloaded from NCBI and analyzed using the limma package to obtain DEGs. Once DEGs were identified, GO and KEGG enrichment analyses were performed as the first step in the bioinformatics process. Subsequently, a protein-protein interaction (PPI) network was constructed according to the common genes in bioinformatics and machine learning using STRING to elucidate the important genes involved in PTC pathogenesis. In machine learning, finding genes entails feature selection to identify the key genes that distinguish biological states. Hybrid feature selection will be used for this. In the second step, the original data sets were preprocessed to detect and correct missing and noisy data; after that, all data were merged. Following performing Linear and Discriminative Hybrid Feature Selection (LDHFS) on the processed dataset, machine learning algorithms such as Random Forest (RF), Naive Bayes (NB), and Support Vector Machines (SVM) are utilized. Bioinformatics and machine learning analyses indicate that the genes RXRG, CDH2, ETV5, QPCT, LRP4, FN1, and LPAR5 are integral to the progression of thyroid cancer. This study attained the highest accuracy utilizing the RF algorithm, achieving an accuracy rate of 94.62%, a Kappa value of 91.36%, and an AUC value of 96.13%. These results offer additional evidence and confirmation for the genetic alterations of these genes. These findings may accelerate the development of prospective therapeutic and diagnostic methods in future research. Bioinformatics and machine learning techniques identified the common genes "RXRG, CDH2, ETV5, QPCT, LRP4, FN1, and LPAR5" as PTC biomarkers, providing novel reference markers for the diagnosis and treatment of PTC patients. The model is anticipated to possess significant predictive value and assist in the early diagnosis and screening of clinical PTC. These insights enhance the field of PTC management and offer guidance for future research.