https://www.rieselprime.de/z/index.php?title=Nomenclature_and_notation&feed=atom&action=historyNomenclature and notation - Revision history2024-03-28T20:15:46ZRevision history for this page on the wikiMediaWiki 1.31.1https://www.rieselprime.de/z/index.php?title=Nomenclature_and_notation&diff=1122&oldid=prevKarbon at 20:32, 14 February 20192019-02-14T20:32:51Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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>:<math>M_x</math> is sometimes used to denote the same function.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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>:<math>M_x</math> is sometimes used to denote the same function.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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>Confusion may sometimes occur when individuals refer to <math>2^{61}-1</math> or <math>2^{127}-1</math> or other [[List of known Mersenne primes|known Mersenne primes]] as M61, <del class="diffchange diffchange-inline">[[</del>M127<del class="diffchange diffchange-inline">]]</del>, or such.  The reader will generally understand that in cases where M'''xx''' is larger than the largest known Mersenne prime, the writer is referring to M'''exponent'''.</div></td><td class='diff-marker'>+</td><td style="color: #222; 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>Confusion may sometimes occur when individuals refer to <math>2^{61}-1</math> or <math>2^{127}-1</math> or other [[List of known Mersenne primes|known Mersenne primes]] as M61, M127, or such.  The reader will generally understand that in cases where M'''xx''' is larger than the largest known Mersenne prime, the writer is referring to M'''exponent'''.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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>==MMxx, MM(xx), and MM<sub>xx</sub> notation==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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>==MMxx, MM(xx), and MM<sub>xx</sub> notation==</div></td></tr>
</table>Karbonhttps://www.rieselprime.de/z/index.php?title=Nomenclature_and_notation&diff=642&oldid=prevKarbon: restored2019-01-30T13:48:53Z<p>restored</p>
<p><b>New page</b></p><div>This serves as a glossary for common terms and the notation that one may encounter in this Wiki.<br />
==Mersenne==<br />
Either [[Marin Mersenne]] or one of the special class of numbers that bear his name.<br />
==[[Mersenne number]]==<br />
Any number whether [[Composite number|composite]] or [[prime]] of the form <math>2^{x}-1</math>. For one of these numbers to be prime, <math>x</math> (the exponent) must also be prime. Thus, the notation of <math>2^{p}-1</math> is generally used when discussing the search for a [[Mersenne prime]].<br />
<br />
==[[Mersenne prime]]==<br />
A number that is itself prime '''and''' can be written in the form <math>2^{x}-1</math>. These are what [[GIMPS]] is searching for.<br />
<br />
==Mxx, M(x), and M<sub>xx</sub> notation==<br />
M'''xx''' can refer to one of 2 different things:<br />
*The '''xx'''th [[Mersenne prime]], in order of size from the smallest to largest. This is the primary and most common usage or<br />
*The '''xx'''th Mersenne prime, in order of discovery (this usage is less common).<br />
<br />
Generally M'''xx''' would be the same in either case, but not so in the case of [[M45]], [[M46]], and [[M47]]. These were discovered in the order of M47, M45 (2 weeks later), then M46 (8 months later.). To avoid confusion, many speakers will use say "The '''xx'''th Mersenne prime found" or "The '''xx'''th known Mersenne prime" to indicate the second case listed above.<br />
<br />
:<math>M(x)</math> is normally used to denote <math>x</math> being run through the Mersenne function: <math>2^{x}-1</math>.<br />
:<math>M_x</math> is sometimes used to denote the same function.<br />
<br />
Confusion may sometimes occur when individuals refer to <math>2^{61}-1</math> or <math>2^{127}-1</math> or other [[List of known Mersenne primes|known Mersenne primes]] as M61, [[M127]], or such. The reader will generally understand that in cases where M'''xx''' is larger than the largest known Mersenne prime, the writer is referring to M'''exponent'''.<br />
<br />
==MMxx, MM(xx), and MM<sub>xx</sub> notation==<br />
The MM'''xx''' notation is used to refer to a '[[Double Mersenne number|Double Mersenne]]' of a number:<br />
:<math>2^{(2^{xx}-1)}-1</math><br />
<br />
Often the parenthesis are not used, but implied, such as [[MM61]] referring to <math>2^{(2^{61}-1)}-1</math><br />
<br />
==HPxx, HP(xx), or HPxx(yy)==<br />
HP<math>xx(yy)</math> refers to a [[Home prime]]. Unless noted with a subscript (for example <math>HPxx_8</math>), it refers to a [[decimal]] or [[base]] 10 home prime. <math>xx</math> is the subject number (the one being tested or being discussed). <math>yy</math> is the step that is being tested or referred to.<br />
<br />
HP<math>xx(yy)=zz</math> or HP<math>xx=zz</math> may be seen. <math>zz</math> can either be referring to the ulimate step value or the home prime for the subject number.<br />
[[Category:Frequently asked questions]]<br />
[[Category:Math]]</div>Karbon