質數魔方陣

ggglgq 发表于 2005-11-24 08:55:10

<P align=center> </P>
<CENTER>
<TABLE border=3>

<TR>
<TD>17</TD>
<TD>89</TD>
<TD>71</TD></TR>
<TR>
<TD>113</TD>
<TD>59</TD>
<TD>5</TD></TR>
<TR>
<TD>47</TD>
<TD>29</TD>
<TD>101</TD></TR></TABLE></CENTER>
<P align=center>3 階質數魔方陣，定和為 177 。</P>
<P align=center>
<HR>

<br>
<P align=center> </P>
<CENTER>
<TABLE border=3>

<TR>
<TD>41</TD>
<TD>71</TD>
<TD>103</TD>
<TD>61</TD></TR>
<TR>
<TD>97</TD>
<TD>79 </TD>
<TD>47 </TD>
<TD>53 </TD></TR>
<TR>
<TD>37</TD>
<TD>67 </TD>
<TD>83 </TD>
<TD>89 </TD></TR>
<TR>
<TD>101 </TD>
<TD>59</TD>
<TD>43</TD>
<TD>73 </TD></TR></TABLE></CENTER>
<P align=center> 4 階質數魔方陣，定和為 276 。</P>
<P align=center> </P>
<P align=center> </P>

ggglgq 发表于 2005-11-24 08:58:12

<P align=center>目前已知定和最小的 3 階連續質數魔方陣： </P>
<CENTER>
<TABLE border=3>

<TR>
<TD>1480028201</TD>
<TD>1480028129 </TD>
<TD>1480028183 </TD></TR>
<TR>
<TD>1480028153</TD>
<TD>1480028171 </TD>
<TD>1480028189 </TD></TR>
<TR>
<TD>1480028159 </TD>
<TD>1480028213</TD>
<TD>1480028141 </TD></TR></TABLE></CENTER>
<P align=center>（連續質數 1480028129 ～ 1480028213 ）</P>
<P align=center> </P>
<P align=center> </P>

ggglgq 发表于 2005-11-24 09:01:01

<P align=center>由 67 ～ 251 所組成的 6 階連續質數魔方陣，其定和為 930： </P>
<P align=center> </P>
<CENTER>
<TABLE border=3>

<TR>
<TD>67 </TD>
<TD>193</TD>
<TD>71</TD>
<TD>251</TD>
<TD>109</TD>
<TD>239 </TD></TR>
<TR>
<TD>139</TD>
<TD>233</TD>
<TD>113</TD>
<TD>181 </TD>
<TD>157 </TD>
<TD>107 </TD></TR>
<TR>
<TD>241</TD>
<TD>97 </TD>
<TD>191 </TD>
<TD>89 </TD>
<TD>163</TD>
<TD>149 </TD></TR>
<TR>
<TD>73 </TD>
<TD>167</TD>
<TD>131 </TD>
<TD>229 </TD>
<TD>151 </TD>
<TD>179 </TD></TR>
<TR>
<TD>199</TD>
<TD>103</TD>
<TD>227 </TD>
<TD>101 </TD>
<TD>127 </TD>
<TD>173 </TD></TR>
<TR>
<TD>211 </TD>
<TD>137</TD>
<TD>197</TD>
<TD>79</TD>
<TD>223</TD>
<TD>83 </TD></TR></TABLE></CENTER>
<P align=center> </P>

ggglgq 发表于 2005-11-24 09:23:16

<P align=center> <FONT size=6><FONT color=#0000ff>質數方陣<BR></P></FONT></FONT>
<P align=center><IMG src="http://sa.ylib.com/circus/images/200307122-1.jpg" border=0></P>
<P> 格盤是一個三階質數方陣，也就是說每列的數（769, 953, 797）與每行的數（797, 659, 937）都是三位數的質數，且各行、各列出現的質數不能重複。</P>

ggglgq 发表于 2005-11-24 09:25:34

<P align=center> <IMG src="http://sa.ylib.com/circus/images/200307122-2.jpg" border=0></P>
<P align=center> 一個四階質數方陣，其中只用到1~9幾個數字。</P>

ggglgq 发表于 2005-11-24 09:29:50

<P align=center> </P>
<P align=center>1 6 4 5 1<BR>4 5 3 8 9<BR>9 2 8 9 3<BR>2 8 0 6 9<BR>9 7 1 7 1</P>
<P align=center>用了全部 0 ~ 9 ，10 個數字的五階質數方陣：<BR></P>

ggglgq 发表于 2005-11-24 09:38:40

<TABLE width=600 align=center>

<TR>
<TD>
<P> 再回到 3 階質數魔方陣。用 100~200 質數為方陣中心，列出所有的 3 階質數魔方陣： </P>
<TR>
<TD>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>139</TD>
<TD>7</TD>
<TD>163</TD></TR>
<TR align=middle>
<TD>127</TD>
<TD>103</TD>
<TD>79</TD></TR>
<TR align=middle>
<TD>43</TD>
<TD>199</TD>
<TD>67</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>139</TD>
<TD>7</TD>
<TD>181</TD></TR>
<TR align=middle>
<TD>151</TD>
<TD>109</TD>
<TD>67</TD></TR>
<TR align=middle>
<TD>37</TD>
<TD>211</TD>
<TD>79</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>157</TD>
<TD>13</TD>
<TD>211</TD></TR>
<TR align=middle>
<TD>181</TD>
<TD>127</TD>
<TD>73</TD></TR>
<TR align=middle>
<TD>43</TD>
<TD>241</TD>
<TD>97</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>157</TD>
<TD>43</TD>
<TD>181</TD></TR>
<TR align=middle>
<TD>151</TD>
<TD>127</TD>
<TD>103</TD></TR>
<TR align=middle>
<TD>73</TD>
<TD>211</TD>
<TD>97</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>173</TD>
<TD>29</TD>
<TD>191</TD></TR>
<TR align=middle>
<TD>149</TD>
<TD>131</TD>
<TD>113</TD></TR>
<TR align=middle>
<TD>71</TD>
<TD>233</TD>
<TD>89</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>173</TD>
<TD>11</TD>
<TD>227</TD></TR>
<TR align=middle>
<TD>191</TD>
<TD>137</TD>
<TD>83</TD></TR>
<TR align=middle>
<TD>47</TD>
<TD>263</TD>
<TD>101</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>199</TD>
<TD>7</TD>
<TD>211</TD></TR>
<TR align=middle>
<TD>151</TD>
<TD>139</TD>
<TD>127</TD></TR>
<TR align=middle>
<TD>67</TD>
<TD>271</TD>
<TD>79</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>191</TD>
<TD>17</TD>
<TD>239</TD></TR>
<TR align=middle>
<TD>197</TD>
<TD>149</TD>
<TD>101</TD></TR>
<TR align=middle>
<TD>59</TD>
<TD>281</TD>
<TD>107</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>193</TD>
<TD>19</TD>
<TD>241</TD></TR>
<TR align=middle>
<TD>199</TD>
<TD>151</TD>
<TD>103</TD></TR>
<TR align=middle>
<TD>61</TD>
<TD>283</TD>
<TD>109</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>163</TD>
<TD>31</TD>
<TD>277</TD></TR>
<TR align=middle>
<TD>271</TD>
<TD>157</TD>
<TD>43</TD></TR>
<TR align=middle>
<TD>37</TD>
<TD>283</TD>
<TD>151</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>197</TD>
<TD>23</TD>
<TD>281</TD></TR>
<TR align=middle>
<TD>251</TD>
<TD>167</TD>
<TD>83</TD></TR>
<TR align=middle>
<TD>53</TD>
<TD>311</TD>
<TD>137</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>197</TD>
<TD>41</TD>
<TD>263</TD></TR>
<TR align=middle>
<TD>233</TD>
<TD>167</TD>
<TD>101</TD></TR>
<TR align=middle>
<TD>71</TD>
<TD>293</TD>
<TD>137</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>233</TD>
<TD>29</TD>
<TD>257</TD></TR>
<TR align=middle>
<TD>197</TD>
<TD>173</TD>
<TD>149</TD></TR>
<TR align=middle>
<TD>89</TD>
<TD>317</TD>
<TD>113</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>257</TD>
<TD>11</TD>
<TD>269</TD></TR>
<TR align=middle>
<TD>191</TD>
<TD>179</TD>
<TD>167</TD></TR>
<TR align=middle>
<TD>89</TD>
<TD>347</TD>
<TD>101</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>251</TD>
<TD>29</TD>
<TD>293</TD></TR>
<TR align=middle>
<TD>233</TD>
<TD>191</TD>
<TD>149</TD></TR>
<TR align=middle>
<TD>89</TD>
<TD>353</TD>
<TD>131</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>233</TD>
<TD>29</TD>
<TD>311</TD></TR>
<TR align=middle>
<TD>269</TD>
<TD>191</TD>
<TD>113</TD></TR>
<TR align=middle>
<TD>71</TD>
<TD>353</TD>
<TD>149</TD></TR></TABLE><br></CENTER>
<CENTER>
<TABLE bgColor=#ffff00 border=1>

<TR align=middle>
<TD>229</TD>
<TD>37</TD>
<TD>313</TD></TR>
<TR align=middle>
<TD>277</TD>
<TD>193</TD>
<TD>109</TD></TR>
<TR align=middle>
<TD>73</TD>
<TD>349</TD>
<TD>157</TD></TR></TABLE><br></CENTER>
<CENTER>共有 17 個符合所求的 3 階質數魔方陣</CENTER></TD></TR>
<UL></UL></TD></TR></TABLE>
<TABLE cellPadding=2 width=600 align=center>

<TR>
<TD></TD></TR></TABLE>
<P> 相关网站请大家参考： <a href="http://www.shes.hcc.edu.tw/~oddest/mq417.htm" target="_blank" >http://www.shes.hcc.edu.tw/~oddest/mq417.htm</A> </P>
<P> </P><br>
[此贴子已经被作者于2005-11-24 9:40:00编辑过]

ggglgq 发表于 2005-11-24 09:43:28

<P> <BR> 通过这几个例子，大家理解“质数方阵”与“质数魔方阵”的区别了吧！<BR> </P>

ggglgq 发表于 2005-11-25 09:32:45

yeah 发表于 2016-8-26 23:43:23

驾考路路通图库

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質數魔方陣