https://michaelnielsen.org/polymath/index.php?action=history&feed=atom&title=Smooth_number 2026-04-13T13:05:07Z Revision history for this page on the wiki MediaWiki 1.42.3 https://michaelnielsen.org/polymath/index.php?title=Smooth_number&diff=2362&oldid=prev 2009-08-20T00:39:12Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:39, 19 August 2009</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An integer is &#039;&#039;S-smooth&#039;&#039; if it does not contain any prime factors less than or equal to S.  The relevance of this concept to the [[finding primes]] project is that if one inserts a non-S-smooth number into a [[factoring|factoring oracle]], one will obtain a prime of size greater than S.  So it would suffice to find a small (and enumerable) set which is guaranteed to contain at least one non-S-smooth number for some large S.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>An integer is &#039;&#039;S-smooth&#039;&#039; if it does not contain any prime factors less than or equal to S.  The relevance of this concept to the [[finding primes]] project is that if one inserts a non-S-smooth number into a [[factoring|factoring oracle]], one will obtain a prime of size greater than S.  So it would suffice to find a small (and enumerable) set which is guaranteed to contain at least one non-S-smooth number for some large S.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># </del>[<del style="font-weight: bold; text-decoration: none;">http</del>:<del style="font-weight: bold; text-decoration: none;">//en.wikipedia.org/wiki/</del>Smooth_number The Wikipedia entry on smooth numbers]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* </ins>[<ins style="font-weight: bold; text-decoration: none;">[wikipedia</ins>:Smooth_number<ins style="font-weight: bold; text-decoration: none;">|</ins>The Wikipedia entry on smooth numbers<ins style="font-weight: bold; text-decoration: none;">]</ins>]</div></td></tr> </table>

Asdf https://michaelnielsen.org/polymath/index.php?title=Smooth_number&diff=2245&oldid=prev 2009-08-08T17:27:25Z

<p>New page: An integer is &#039;&#039;S-smooth&#039;&#039; if it does not contain any prime factors less than or equal to S. The relevance of this concept to the <a href="/polymath/index.php?title=Finding_primes" title="Finding primes">finding primes</a> project is that if one inserts a non-S...</p> <p><b>New page</b></p><div>An integer is &#039;&#039;S-smooth&#039;&#039; if it does not contain any prime factors less than or equal to S. The relevance of this concept to the [[finding primes]] project is that if one inserts a non-S-smooth number into a [[factoring|factoring oracle]], one will obtain a prime of size greater than S. So it would suffice to find a small (and enumerable) set which is guaranteed to contain at least one non-S-smooth number for some large S.<br /> <br /> # [http://en.wikipedia.org/wiki/Smooth_number The Wikipedia entry on smooth numbers]</div>

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