The invention provides a method of priming T cells against tumor antigens comprising by obtaining nanullve CD4null or CD8null T cells from at least one healthy individual, obtaining at least one protein or peptide from at least one cancerous cell; obtaining antigen presenting cells (APCs), culturing the APCs with the at least one protein or peptide, and adding the T cells to the culture of the APCs. The primed T cells can then be employed to identify the antigens or therapeutically as prophylaxis or treatment for cancers. The invention also provides cyclin molecules, and fragments derived from cyclin molecules, as tumor antigens. The invention provides a method for diagnosing a malignant or pre-malignant condition within a patient. The invention also provides a method for vaccinating a patient against malignancies comprising introducing a protein or peptide consisting essentially of all or an immunogenic fragment of a cyclin protein into the patient.