{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T17:00:58Z","timestamp":1778000458912,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T00:00:00Z","timestamp":1553126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper deals with the hidden structure of prime numbers. Previous numerical studies have already indicated a fractal-like behavior of prime-indexed primes. The construction of binary images enables us to generalize this result. In fact, two-integer sequences can easily be converted into a two-color image. In particular, the resulting method shows that both the coprimality condition and Ramanujan primes resemble the Minkowski island and Cantor set, respectively. Furthermore, the comparison between prime-indexed primes and Ramanujan primes is introduced and discussed. Thus the Cantor set covers a relevant role in the fractal-like description of prime numbers. The results confirm the feasibility of the method based on binary images. The link between fractal sets and chaotic dynamical systems may allow the characterization of the H\u00e9non map only in terms of prime numbers.<\/jats:p>","DOI":"10.3390\/e21030304","type":"journal-article","created":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T12:28:01Z","timestamp":1553171281000},"page":"304","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":160,"title":["Primality, Fractality, and Image Analysis"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3320-1493","authenticated-orcid":false,"given":"Emanuel","family":"Guariglia","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applications \u201cR. Caccioppoli\u201d, University of Naples Federico II, 80126 Naples, Italy"},{"name":"School of Economics, Management and Statistics, University of Bologna, 40126 Bologna, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,21]]},"reference":[{"key":"ref_1","unstructured":"Guy, R. (2010). Unsolved Problems in Number Theory, Springer."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nash, J.F., and Rassias, M.T. (2016). Open Problems in Mathematics, Springer.","DOI":"10.1007\/978-3-319-32162-2"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.tcs.2014.05.025","article-title":"Quantum cryptography: Public key distribution and coin tossing","volume":"560","author":"Bennet","year":"2014","journal-title":"Theor. Comput. 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