{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:38:55Z","timestamp":1776724735920,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"225","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We give numerical and theoretical evidence in support of the conjecture of Dressler that between any two positive integers having the same prime factors there is a prime. In particular, it is shown that the abc conjecture implies that the gap between two consecutive such numbers\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"a greater-than c\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">a &gt;c<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"much-greater-than a Superscript 1 slash 2 minus epsilon\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u226b\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>a<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mi>\n                                  \u03f5\n                                  \n                                <\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\gg a^{1\/2 - \\epsilon }<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and it is shown that this lower bound is best possible. Dressler\u2019s conjecture is verified for values of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"a\">\n                        <mml:semantics>\n                          <mml:mi>a<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">a<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"c\">\n                        <mml:semantics>\n                          <mml:mi>c<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">c<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    up to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"7 dot 10 Superscript 13\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>7<\/mml:mn>\n                            <mml:mo>\n                              \u22c5\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>10<\/mml:mn>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>13<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">7\\cdot 10^{13}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-99-01024-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"395-401","source":"Crossref","is-referenced-by-count":3,"title":["Gaps between integers with the same prime factors"],"prefix":"10.1090","volume":"68","author":[{"given":"Todd","family":"Cochrane","sequence":"first","affiliation":[]},{"given":"Robert","family":"Dressler","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1999]]},"reference":[{"issue":"152","key":"1","doi-asserted-by":"publisher","first-page":"1435","DOI":"10.2307\/2006409","article-title":"The first occurrence of certain large prime gaps","volume":"35","author":"Brent, Richard P.","year":"1980","journal-title":"Math. 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Cram\u00e9r, On the order of magnitude of the difference between consecutive prime numbers, Acta Arith. 2 (1937), 23\u201346.","DOI":"10.4064\/aa-2-1-23-46"},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/0019-3577(92)90045-M","article-title":"Exponential Diophantine equations with four terms","volume":"3","author":"Mo, De Ze","year":"1992","journal-title":"Indag. Math. (N.S.)","ISSN":"https:\/\/id.crossref.org\/issn\/0019-3577","issn-type":"print"},{"key":"6","doi-asserted-by":"publisher","first-page":"483","DOI":"10.2307\/2003253","article-title":"On first appearance of prime differences","volume":"21","author":"Lander, L. J.","year":"1967","journal-title":"Math. 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