MaplePrimes

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    <title>MaplePrimes - comments on Post, MRB constant N part 3</title>
    <link>http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3</link>
    <language>en-us</language>
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    <lastBuildDate>Sat, 13 Jun 2026 18:47:15 GMT</lastBuildDate>
    <pubDate>Sat, 13 Jun 2026 18:47:15 GMT</pubDate>
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    <itunes:summary />
    <description>The latest comments added to the Post, MRB constant N part 3</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - comments on Post, MRB constant N part 3</title>
      <link>http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3</link>
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    <item>
      <title>Below we have approximations involving the</title>
      <link>http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3?ref=Feed:MaplePrimes:MRB constant N part 3:Comments#comment134515</link>
      <itunes:summary>&lt;p&gt;&lt;span&gt;Below we have approximations involving the MRB constant. The MRB constant plus a fraction is saved as P while a combination of another constant is saved as Q. We then subtract Q from P and always have a very small result.&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Let&lt;/p&gt;
&lt;p&gt;&lt;span&gt;Let c be the MRB constant, 0.1878596424620671202485179340542732300559030949001387.&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;P:=&amp;nbsp;c+7/47&lt;/p&gt;
&lt;p&gt;Let G be&amp;nbsp;&lt;a href="http://mathworld.wolfram.com/GrahamsBiggestLittleHexagon.html"&gt;Graham's Biggest Little Hexagon area&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;G:=0.6749814429301047036884958318514002889802977322780266&lt;/p&gt;
&lt;p&gt;Q:=(79-940*G)/(3530*G-4032)&lt;/p&gt;
&lt;p&gt;p-Q=&amp;nbsp;-3.3803*10^(-18)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P := c+9/46&lt;/p&gt;
&lt;p&gt;Let Q be the positive root of&amp;nbsp;41309050*x^3-2330137&lt;/p&gt;
&lt;p&gt;Q:=0.3835118163751105434087&lt;/p&gt;
&lt;p&gt;P-Q=5.51007*10^(-17)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+46/47&lt;/p&gt;
&lt;p&gt;Let p be the &lt;a href="http://mathworld.wolfram.com/PlasticConstant.html["&gt;plastic constant&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;p:=1.3247179572447460259609088544780973407344040569017333&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Q:=-5*(37*p-2196)/(7000*p-71)&lt;/p&gt;
&lt;p&gt;p-Q=6.97*10^(-19)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+35/48&lt;/p&gt;
&lt;p&gt;e:=evalf(exp(1))&lt;/p&gt;
&lt;p&gt;Q:= -17(e-5)*(5*e-6)/(-751+215*e+66*e^2)&lt;/p&gt;
&lt;p&gt;P-Q=&amp;nbsp;-1.710*10^(-19)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+40/49&lt;/p&gt;
&lt;p&gt;Let r be the &lt;a href="http://mathworld.wolfram.com/RabbitConstant.html"&gt;rabbit constant&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;r:=0.7098034428612913146417873994445755970125022057678605&lt;/p&gt;
&lt;p&gt;Q:=6*(167*r+1060)/(25*r+7024)&lt;/p&gt;
&lt;p&gt;P-Q=&amp;nbsp;-1.20*10^(-19)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+29/51&lt;/p&gt;
&lt;p&gt;Let Pg be &lt;a href="http://mathworld.wolfram.com/PlouffesConstants.html"&gt;plouffe's gamma constant&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;Pg:=0.1475836176504332741754010762247405259511345238869178&lt;/p&gt;
&lt;p&gt;Q:=-20*(303Pg-40)/(178Pg-151)&lt;/p&gt;
&lt;p&gt;P-Q=-1.12336*10^(-17)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+15/17&lt;/p&gt;
&lt;p&gt;Let F be the &lt;a href="http://mathworld.wolfram.com/Fransen-RobinsonConstant.html"&gt;Frans&amp;eacute;n-Robinson Constant&lt;/a&gt;,&lt;/p&gt;
&lt;p&gt;F:=2.8077702420285193652215011865577729323080859209301982&lt;/p&gt;
&lt;p&gt;Q:=(20882-2007*F)/(1050 + 4700*F)&lt;/p&gt;
&lt;p&gt;P-Q=&amp;nbsp;-1.739*10^(-18)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+37/52&lt;/p&gt;
&lt;p&gt;Let QRS be the &lt;a href="http://mathworld.wolfram.com/QRSConstant.html"&gt;QRS constant&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;QRS:=0.6054436571967327494789228424472074752208994969563226&lt;/p&gt;
&lt;p&gt;Q:=(3970*QRS+83)/(6053*QRS-900)&lt;/p&gt;
&lt;p&gt;P-Q=1.7719*10^(-18)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+43/52&lt;/p&gt;
&lt;p&gt;Let f1 be the &lt;a href="http://mathworld.wolfram.com/FoiasConstant.html"&gt;first Foias constant&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;f1:=2.2931662874118610315080282912508058643722572903271212&lt;/p&gt;
&lt;p&gt;Q:=(3881-220*f1)/(100*f1+3098)&lt;/p&gt;
&lt;p&gt;P-Q=&amp;nbsp;-3.670*10^(-18)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;P:=c+16/53&lt;/p&gt;
&lt;p&gt;Let Pa be &lt;a href="http://mathworld.wolfram.com/PlouffesConstants.html"&gt;Plouffe's A constant&lt;/a&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Pa:=0.1591549430918953357688837633725143620344596457404564&lt;/p&gt;
&lt;p&gt;Q:=4*(5800Pa-773)/(6000Pa+271)&lt;/p&gt;
&lt;p&gt;P-Q=4.6241*10^(-18)&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 3</description>
      <guid>134515</guid>
      <pubDate>Fri, 25 May 2012 02:03:21 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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    <item>
      <title>&amp;nbsp;Again let c be the MRB constant and</title>
      <link>http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3?ref=Feed:MaplePrimes:MRB constant N part 3:Comments#comment134536</link>
      <itunes:summary>&lt;p&gt;Digits:=22&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Again let c be the MRB constant and this time let b be&lt;a href="http://mathworld.wolfram.com/BirthdayProblem.html"&gt;&amp;nbsp;the probability that at least two people in a room of 23 share&amp;nbsp;birthday.&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;b:=.5072972343239854072254172283370325002359718452929878&lt;br&gt;c:=&amp;nbsp;0.187859642462067120248517934054273230055903094900139&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;(6200 b-239)/(2 (1550 b+437))-1 =0.187859642462067125421&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;(5 (1860 b+127))/(2 (1550 b+437))-2 =0.187859642462067125421&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;(5 (4960 b+1001))/(2 (1550 b+437))-7 =&amp;nbsp;0.187859642462067125421&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;0.187859642462067125421-c =&amp;nbsp;5.1725*10^(-18)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;Also&amp;nbsp;&lt;/p&gt;
&lt;p&gt;evalf(23212425209 /3144920904*Pi-23 - c) =&amp;nbsp;2.*10^(-20)&lt;/p&gt;
&lt;!--break--&gt;
&lt;p&gt;&amp;nbsp;and&lt;/p&gt;
&lt;p&gt;&amp;nbsp;evalf(20561436223 /2375900782*Pi-27 - c) =&amp;nbsp;3.*10^(-20)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Also&lt;/p&gt;
&lt;p&gt;evalf((-216+53*Pi^(1/2)+363*Pi+1526*Pi^(3/2)+1062*Pi^2)/(92*Pi)-69-c) =&amp;nbsp;-3.*10^(-20)&lt;/p&gt;
&lt;p&gt;and&lt;/p&gt;
&lt;p&gt;evalf(1/890*(115850*Zeta(3)+10010*Zeta(5)-1785*Pi^2-979*Pi^4)-41-c) =&amp;nbsp;-5.*10^(-20)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;and&lt;/p&gt;
&lt;p&gt;evalf((6/11)*Pi*arccosh(292945824/1726159)^2-58-c) =&amp;nbsp;6.*10^(-20)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://marvinrayburns.com"&gt;marvinrayburns.com&lt;br&gt;&lt;/a&gt;&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 3</description>
      <guid>134536</guid>
      <pubDate>Fri, 25 May 2012 19:28:38 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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      <title>Digits := 23Let c be the MRB constantc</title>
      <link>http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3?ref=Feed:MaplePrimes:MRB constant N part 3:Comments#comment134542</link>
      <itunes:summary>&lt;p&gt;Digits := 23&lt;/p&gt;
&lt;p&gt;Let c be the MRB constant&lt;/p&gt;
&lt;p&gt;c := .187859642462067120248517934054273230055903094900139&lt;/p&gt;
&lt;p&gt;Let C be &lt;a href="http://mathworld.wolfram.com/CatalansConstant.html"&gt;Catalan's Constant&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;C := .9159655941772190150546035149323841107741493742816721&lt;/p&gt;
&lt;p&gt;evalf(-(119/19)*C-115+(479561360045/59753497176)*Pi+(525/76)*Pi^2+(102/19)*Pi*ln(2)+(353/76)*Pi*ln(3)-2*c)&amp;nbsp;=&amp;nbsp;-8.*10^(-21)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;Digits:=24&lt;/p&gt;
&lt;p&gt;c := .187859642462067120248517934054273230055903094900139&lt;/p&gt;
&lt;p&gt;evalf((2/7163)*(-90155*e-29388+37921*e^2)/(e*Pi)-c)&amp;nbsp;= -5.19*10^(-22)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;evalf(((1325323718/907073065)*Pi-4)/Pi-c) =&amp;nbsp;-2.6*10^(-22)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 3</description>
      <guid>134542</guid>
      <pubDate>Sat, 26 May 2012 05:38:18 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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    <item>
      <title>Digits:=20Let c be the MRB constant.Let</title>
      <link>http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3?ref=Feed:MaplePrimes:MRB constant N part 3:Comments#comment134584</link>
      <itunes:summary>&lt;pre&gt;Digits:=20&lt;/pre&gt;
&lt;pre&gt;Let c be the MRB constant.&lt;/pre&gt;
&lt;pre&gt;Let V be the &lt;a href="http://mathworld.wolfram.com/FigureEightKnot.html"&gt;figure eight hyperbolic volume&lt;/a&gt;.&lt;/pre&gt;
&lt;pre&gt;c := .1878596424620671202485179340542732300559030949001387&lt;/pre&gt;
&lt;pre&gt;V := 2.0298832128193072500424051085490405&lt;/pre&gt;
&lt;pre&gt;(15*(V+667))/(839*V+2605)  = 2.329452296051860367745&lt;/pre&gt;
&lt;pre&gt;evalf(c+Pi-1)              = 2.329452296051860358712&lt;/pre&gt;
&lt;pre&gt;Let p be the &lt;a href="http://mathworld.wolfram.com/PrimeConstant.html"&gt;prime constant&lt;/a&gt;.&lt;/pre&gt;
&lt;pre&gt;p := .4146825098511116602481096221543077083657742381379&lt;/pre&gt;
&lt;pre&gt;(9509-169*p)/(50*(18*p+23)) = 6.196711067333514470392&lt;/pre&gt;
&lt;pre&gt;evalf(c+7*(4-Pi))           = 6.19671106733351445101&lt;/pre&gt;
&lt;pre&gt;&amp;nbsp;&lt;/pre&gt;
&lt;pre&gt;Digits := 53&lt;/pre&gt;
&lt;pre&gt;c := .187859642462067120248517934054273230055903094900138786172&lt;/pre&gt;
&lt;pre&gt;evalf(17Pi-642614815285663014792765/12074864494484015995117-c) = -1.*10^(-51)&lt;/pre&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 3</description>
      <guid>134584</guid>
      <pubDate>Mon, 28 May 2012 02:26:09 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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