{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T03:04:42Z","timestamp":1782270282574,"version":"3.54.5"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $S=(d_1,d_2,d_3, \\ldots )$ be an infinite sequence of rolls of independent fair dice. For an integer $k \\geq 1$, let $L_k=L_k(S)$ be the smallest $i$ so that there are $k$ integers $j \\leq i$ for which $\\sum_{t=1}^j d_t$ is a prime. Therefore, $L_k$ is the random variable whose value is the number of dice rolls required until the accumulated sum equals a prime $k$ times. It is known that the expected value of $L_1$ is close to $2.43$. Here we show that for large $k$, the expected value of $L_k$ is $(1+o(1)) k\\log_e k$, where the $o(1)$-term tends to zero as $k$ tends to infinity. We also include some computational results about the distribution of $L_k$ for $k \\leq 100$.<\/jats:p>","DOI":"10.37236\/13878","type":"journal-article","created":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T22:53:39Z","timestamp":1761000819000},"source":"Crossref","is-referenced-by-count":1,"title":["Hitting $k$ Primes by Dice Rolls"],"prefix":"10.37236","volume":"32","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaakov","family":"Malinovsky","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lucy","family":"Martinez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Doron","family":"Zeilberger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2025,10,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p16\/code","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T22:53:39Z","timestamp":1761000819000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i4p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/13878","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,17]]},"article-number":"P4.16"}}