In Knuths up-arrow notation, 2 ↑↑ 2 = 2 ↑↑↑ 2 = 4, and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically three. The sum of the first four prime numbers two + three + five + seven is the only sum of four consecutive prime numbers that yields an odd prime number, seventeen, which is the fourth super-prime. Four lies between the first proper pair of twin primes, three and five, which are the first two Fermat primes, like seventeen, which is the third.
Li and Fraumeni identified four families in which siblings or cousins of rhabdomyosarcoma patients had a childhood sarcoma, which suggested a familial cancer syndrome. Identification of TP53s the gene affected by mutation was suggested by the same approach. Over half of the cancers in LFS families had been previously associated with inactivating mutations of the p53 gene and in one primary research study, DNA sequencing in samples taken from five Li–Fraumeni syndrome families showed autosomal dominant inheritance of a mutated TP53 gene. See also
OSLAM syndrome

References
Further reading
Li–Fraumeni Syndrome by Katherine Schneider, MPH, Kristin Zelley, MS, Kim E Nichols, MD and Judy Garber, MD, MPH, in GeneReviews, a section of GeneTests, published online by the University of Washington with funds from the National Institutes of Health
Li–Fraumeni syndrome, in the National Library of Medicine
Li–Fraumeni syndrome; LFS1, entry in Online Mendelian Inheritance in Man (OMIM), published by Johns Hopkins University and the National Institutes of Health