{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T02:09:29Z","timestamp":1768529369047,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T00:00:00Z","timestamp":1719964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In a landscape where interest in prime sieving has waned and practitioners are few, we are still hoping for a domain renaissance, fueled by a resurgence of interest and a fresh wave of innovation. Building upon years of extensive research and experimentation, this article aims to contribute by presenting a heterogeneous compilation of generic tweaks and boosters aimed at revitalizing prime sieving methodologies. Drawing from a wealth of resurfaced knowledge and refined sieving algorithms, techniques, and optimizations, we unveil a diverse array of strategies designed to elevate the efficiency, accuracy, and scalability of prime sieving algorithms; these tweaks and boosters represent a synthesis of old wisdom and new discoveries, offering practical guidance for researchers and practitioners alike.<\/jats:p>","DOI":"10.3390\/a17070291","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T08:45:34Z","timestamp":1719996334000},"page":"291","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Prime Time Tactics\u2014Sieve Tweaks and Boosters"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-0185-143X","authenticated-orcid":false,"given":"Mircea","family":"Ghidarcea","sequence":"first","affiliation":[{"name":"Computer Science Department, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania"}]},{"given":"Decebal","family":"Popescu","sequence":"additional","affiliation":[{"name":"Computer Science Department, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1145\/366199.366257","article-title":"Algorithm 35: Sieve","volume":"4","author":"Wood","year":"1961","journal-title":"Commun. ACM"},{"key":"ref_2","unstructured":"D\u2019Ooge., M.L. (1926). Introduction to Arithmetic, Macmillan."},{"key":"ref_3","first-page":"73","article-title":"Sundaram\u2019s Sieve for Prime Numbers","volume":"2","author":"Aiyar","year":"1934","journal-title":"Math. Stud."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Helfgott, H.A. (2019). An Improved Sieve of Eratosthenes. arXiv.","DOI":"10.1090\/mcom\/3438"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1145\/363566.363689","article-title":"Algorithm 310: Prime Number Generator 1","volume":"10","author":"Chartres","year":"1967","journal-title":"Commun. ACM"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1145\/363566.363692","article-title":"Algorithm 311: Prime Number Generator 2","volume":"10","author":"Charters","year":"1967","journal-title":"Commun. ACM"},{"key":"ref_7","first-page":"563","article-title":"Algorithm 356: A Prime Number Generator Using the Treesort Principle [A1]","volume":"12","author":"Singleton","year":"1969","journal-title":"Commun. ACM"},{"key":"ref_8","first-page":"563","article-title":"Algorithm 357: An Efficient Prime Number Generator [A1]","volume":"12","author":"Singleton","year":"1969","journal-title":"Commun. ACM"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1145\/359810.359838","article-title":"Some New Upper Bounds on the Generation of Prime Numbers","volume":"20","author":"Mairson","year":"1977","journal-title":"Commun. ACM"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1145\/359657.359660","article-title":"A Linear Sieve Algorithm for Finding Prime Numbers","volume":"21","author":"Gries","year":"1978","journal-title":"Commun. ACM"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1145\/357121.357128","article-title":"An Exercise in Program Explanation","volume":"3","author":"Misra","year":"1981","journal-title":"Acm Trans. Program. Lang. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1145\/358527.358540","article-title":"A Sublinear Additive Sieve for Finding Prime Number","volume":"24","author":"Pritchard","year":"1981","journal-title":"Commun. ACM"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/BF00264164","article-title":"Explaining the Wheel Sieve","volume":"17","author":"Pritchard","year":"1982","journal-title":"Acta Inform."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Paul Pritchard (1983). Fast Compact Prime Number Sieves (among Others). J. Algorithms, 4, 332\u2013344.","DOI":"10.1016\/0196-6774(83)90014-7"},{"key":"ref_15","first-page":"17","article-title":"Linear Prime-Number Sieves: A Family Tree","volume":"9","author":"Pritchard","year":"1987","journal-title":"Sci. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pritchard, P. (1994). Improved Incremental Prime Number Sieves, Springer. Tech. Rep.","DOI":"10.1007\/3-540-58691-1_67"},{"key":"ref_17","unstructured":"Sorenson, J. (1990). An Introduction to Prime Number Sieves, University of Wisconsin- Madison, Computer Sciences Department. Tech. Rep."},{"key":"ref_18","unstructured":"Sorenson, J. (1991). An Analysis of Two Prime Number Sieves, University of Wisconsin- Madison, Computer Sciences Department. Tech. Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1006\/inco.1994.1082","article-title":"2 Fast Parallel Prime Number Sieves","volume":"114","author":"Sorenson","year":"1994","journal-title":"Inf. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Sorenson, J. (1998). Trading Time for Space in Prime Number Sieves, Springer. Tech. Rep.","DOI":"10.1007\/BFb0054861"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1090\/S0025-5718-03-01501-1","article-title":"Prime Sieves Using Binary Quadratic Forms","volume":"73","author":"Atkin","year":"2003","journal-title":"Math. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ghidarcea, M., and Popescu, D. (2024). Prime Number Sieving\u2014A Systematic Review with Performance Analysis. Algorithms, 17.","DOI":"10.3390\/a17040157"},{"key":"ref_23","first-page":"15","article-title":"Sieve of Atkin Revisited","volume":"86","author":"Ghidarcea","year":"2024","journal-title":"Sci. Bull. Univ. Politeh. Buchar."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"36","DOI":"10.61416\/ceai.v26i1.8860","article-title":"Static Wheels in Fast Sieves","volume":"26","author":"Ghidarcea","year":"2024","journal-title":"J. Control Eng. Appl. Inform."},{"key":"ref_25","unstructured":"Walisch, K. (2024, June 11). Primesieve. Available online: https:\/\/github.com\/kimwalisch\/primesieve."},{"key":"ref_26","unstructured":"Oliveira e Silva, T. (2024, June 11). Fast Implementation of the Segmented Sieve of Eratosthenes. Available online: https:\/\/sweet.ua.pt\/tos\/software\/prime_sieve.html."},{"key":"ref_27","unstructured":"Seizert, C. (2024, June 11). CUDASieve. Available online: https:\/\/github.com\/curtisseizert\/CUDASieve."},{"key":"ref_28","first-page":"111","article-title":"Faster Population Counts Using AVX2 Instructions","volume":"61","author":"Kurz","year":"2017","journal-title":"Comput. J."},{"key":"ref_29","unstructured":"Bernstein, D.J. (2024, June 11). Primegen. Available online: https:\/\/cr.yp.to\/primegen.html."},{"key":"ref_30","unstructured":"Flammenkamp, A. (2024, June 11). Sieve of Eratosthenes. Available online: https:\/\/wwwhomes.uni-bielefeld.de\/achim\/prime_sieve.html."},{"key":"ref_31","unstructured":"Walisch, K. (2024, June 11). Speaker: Kim Walisch. Available online: https:\/\/primzahlen.de\/referenten\/Kim_Walisch\/index2.htm."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/7\/291\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:09:34Z","timestamp":1760108974000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/7\/291"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,3]]},"references-count":31,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["a17070291"],"URL":"https:\/\/doi.org\/10.3390\/a17070291","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,3]]}}}