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We also consider\n                    <jats:italic>thickened prime components<\/jats:italic>\n                    , which are augmented by all circles immediately tangent to the prime component. In both cases, we ask about the curvatures which appear. We consider the residue classes attained by the set of curvatures, the number of circles in such components, the number of distinct integers occurring as curvatures and the number of prime components in a packing. As part of our investigation, we computed and analysed example components up\u00a0to around curvature\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$10^{13}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msup>\n                            <mml:mn>10<\/mml:mn>\n                            <mml:mn>13<\/mml:mn>\n                          <\/mml:msup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    ; software is available.\n                  <\/jats:p>","DOI":"10.1007\/978-3-032-11183-8_8","type":"book-chapter","created":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T22:15:30Z","timestamp":1780524930000},"page":"183-233","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Prime and\u00a0Thickened Prime Components in\u00a0Apollonian Circle Packings"],"prefix":"10.1007","author":[{"given":"Holley","family":"Friedlander","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elena","family":"Fuchs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Piper","family":"Harris","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Catherine","family":"Hsu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Rickards","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Katherine","family":"Sanden","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Damaris","family":"Schindler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Katherine E.","family":"Stange","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,4]]},"reference":[{"key":"8_CR1","doi-asserted-by":"crossref","unstructured":"Soren\u00a0Laing Aletheia-Zomlefer, Lenny Fukshansky, and Stephan\u00a0Ramon Garcia. 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