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14 <a name="package-MathUtil-"></a> 1 <span class="k">package </span><span class="i">MathUtil</span><span class="sc">;</span>
15 2 <span class="c">#</span>
16 3 <span class="c"># $RCSfile: MathUtil.pm,v $</span>
17 4 <span class="c"># $Date: 2015/02/28 20:47:17 $</span>
18 5 <span class="c"># $Revision: 1.28 $</span>
19 6 <span class="c">#</span>
20 7 <span class="c"># Author: Manish Sud &lt;msud@san.rr.com&gt;</span>
21 8 <span class="c">#</span>
22 9 <span class="c"># Copyright (C) 2015 Manish Sud. All rights reserved.</span>
23 10 <span class="c">#</span>
24 11 <span class="c"># This file is part of MayaChemTools.</span>
25 12 <span class="c">#</span>
26 13 <span class="c"># MayaChemTools is free software; you can redistribute it and/or modify it under</span>
27 14 <span class="c"># the terms of the GNU Lesser General Public License as published by the Free</span>
28 15 <span class="c"># Software Foundation; either version 3 of the License, or (at your option) any</span>
29 16 <span class="c"># later version.</span>
30 17 <span class="c">#</span>
31 18 <span class="c"># MayaChemTools is distributed in the hope that it will be useful, but without</span>
32 19 <span class="c"># any warranty; without even the implied warranty of merchantability of fitness</span>
33 20 <span class="c"># for a particular purpose. See the GNU Lesser General Public License for more</span>
34 21 <span class="c"># details.</span>
35 22 <span class="c">#</span>
36 23 <span class="c"># You should have received a copy of the GNU Lesser General Public License</span>
37 24 <span class="c"># along with MayaChemTools; if not, see &lt;http://www.gnu.org/licenses/&gt; or</span>
38 25 <span class="c"># write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,</span>
39 26 <span class="c"># Boston, MA, 02111-1307, USA.</span>
40 27 <span class="c">#</span>
41 28
42 29 <span class="k">use</span> <span class="w">strict</span><span class="sc">;</span>
43 30 <span class="k">use</span> <span class="w">Exporter</span><span class="sc">;</span>
44 31 <span class="k">use</span> <span class="w">Constants</span><span class="sc">;</span>
45 32 <span class="k">use</span> <span class="w">Math::Trig</span> <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
46 33 <span class="k">use</span> <span class="w">POSIX</span> <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
47 34
48 35 <span class="k">use</span> <span class="w">vars</span> <span class="q">qw(@ISA @EXPORT @EXPORT_OK %EXPORT_TAGS)</span><span class="sc">;</span>
49 36
50 37 <span class="i">@ISA</span> = <span class="q">qw(Exporter)</span><span class="sc">;</span>
51 38 <span class="i">@EXPORT</span> = <span class="q">qw(acos asin atan tan ceil floor log10 min max srandom random round GeneratePrimeNumbersUpToLimit GeneratePrimeNumbersUpToCount)</span><span class="sc">;</span>
52 39 <span class="i">@EXPORT_OK</span> = <span class="q">qw()</span><span class="sc">;</span>
53 40
54 41 <span class="i">%EXPORT_TAGS</span> = <span class="s">(</span><span class="w">all</span> <span class="cm">=&gt;</span> <span class="s">[</span><span class="i">@EXPORT</span><span class="cm">,</span> <span class="i">@EXPORT_OK</span><span class="s">]</span>
55 42 <span class="s">)</span><span class="sc">;</span>
56 43
57 44
58 45 <span class="c"># Return next largest integer...</span>
59 <a name="ceil-"></a> 46 <span class="k">sub </span><span class="m">ceil ($)</span> <span class="s">{</span>
60 47 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
61 48
62 49 <span class="k">return</span> <span class="i">POSIX::ceil</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
63 50 <span class="s">}</span>
64 51
65 52 <span class="c"># Return previous smallest integer...</span>
66 <a name="floor-"></a> 53 <span class="k">sub </span><span class="m">floor ($)</span> <span class="s">{</span>
67 54 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
68 55
69 56 <span class="k">return</span> <span class="i">POSIX::floor</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
70 57 <span class="s">}</span>
71 58
72 59 <span class="c"># Calculate log value using base 10...</span>
73 <a name="log10-"></a> 60 <span class="k">sub </span><span class="m">log10 ($)</span> <span class="s">{</span>
74 61 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
75 62
76 63 <span class="k">return</span> <span class="i">CORE::</span><span class="k">log</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span>/<span class="i">CORE::</span><span class="k">log</span><span class="s">(</span><span class="n">10</span><span class="s">)</span><span class="sc">;</span>
77 64 <span class="s">}</span>
78 65
79 66 <span class="c"># Return the smaller of two numbers...</span>
80 <a name="min-"></a> 67 <span class="k">sub </span><span class="m">min ($$)</span> <span class="s">{</span>
81 68 <span class="k">my</span><span class="s">(</span><span class="i">$Value1</span><span class="cm">,</span> <span class="i">$Value2</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
82 69
83 70 <span class="k">return</span> <span class="s">(</span><span class="i">$Value1</span> &lt;= <span class="i">$Value2</span><span class="s">)</span> ? <span class="i">$Value1</span> <span class="co">:</span> <span class="i">$Value2</span><span class="sc">;</span>
84 71 <span class="s">}</span>
85 72
86 73 <span class="c"># Return the larger of two numbers...</span>
87 <a name="max-"></a> 74 <span class="k">sub </span><span class="m">max ($$)</span> <span class="s">{</span>
88 75 <span class="k">my</span><span class="s">(</span><span class="i">$Value1</span><span class="cm">,</span> <span class="i">$Value2</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
89 76
90 77 <span class="k">return</span> <span class="s">(</span><span class="i">$Value1</span> &gt;= <span class="i">$Value2</span><span class="s">)</span> ? <span class="i">$Value1</span> <span class="co">:</span> <span class="i">$Value2</span><span class="sc">;</span>
91 78 <span class="s">}</span>
92 79
93 80 <span class="c"># The random number generator implemented in MayaChemTools is a variant of linear</span>
94 81 <span class="c"># congruential generator (LCG) as described by Miller et al. [ Ref 120 ]. It is</span>
95 82 <span class="c"># also referred to as Lehmer random number generator or Park-Miller random number</span>
96 83 <span class="c"># generator.</span>
97 84 <span class="c">#</span>
98 85 <span class="c"># Unlike Perl&#39;s core random number generator function rand, the random number</span>
99 86 <span class="c"># generator implemented in MayaChemTools generates consistent random values</span>
100 87 <span class="c"># across different platforms - Windows, CygWin, Linux, Unix - for a specific random</span>
101 88 <span class="c"># seed.</span>
102 89 <span class="c">#</span>
103 90
104 91 <span class="c"># $RandomModulus = 2**31 - 1;</span>
105 92 <span class="c"># $RandomMultiplier = 16807;</span>
106 93 <span class="c"># $RandomQuotient = $RandomModulus / $RandomMultiplier;</span>
107 94 <span class="c"># $RandomRemainder = $RandomModulus % $RandomMultiplier</span>
108 95 <span class="c">#</span>
109 96 <span class="c"># $MaxRandomSeed = 2*31 -2</span>
110 97 <span class="c">#</span>
111 98 <span class="k">my</span><span class="s">(</span><span class="i">$MaxRandomSeed</span><span class="cm">,</span> <span class="i">$RandomSeed</span><span class="cm">,</span> <span class="i">$RandomModulus</span><span class="cm">,</span> <span class="i">$RandomMultiplier</span><span class="cm">,</span> <span class="i">$RandomQuotient</span><span class="cm">,</span> <span class="i">$RandomRemainder</span><span class="s">)</span><span class="sc">;</span>
112 99
113 100 <span class="i">$MaxRandomSeed</span> = <span class="n">2147483646</span><span class="sc">;</span>
114 101 <span class="i">$RandomSeed</span> = <span class="n">123456789</span><span class="sc">;</span>
115 102
116 103 <span class="i">$RandomModulus</span> = <span class="n">2147483647</span><span class="sc">;</span>
117 104 <span class="i">$RandomMultiplier</span> = <span class="n">16807</span><span class="sc">;</span>
118 105 <span class="i">$RandomQuotient</span> = <span class="n">127773</span><span class="sc">;</span>
119 106 <span class="i">$RandomRemainder</span> = <span class="n">2836</span><span class="sc">;</span>
120 107
121 108 <span class="c"># Set random number seed...</span>
122 109 <span class="c">#</span>
123 110 <span class="c"># The intial value of random number seed is recommeded to be an integer between 1</span>
124 111 <span class="c"># and 2**31 - 2 [Ref 120] which translates to be 1 and 2147483646</span>
125 112 <span class="c">#</span>
126 <a name="srandom-"></a> 113 <span class="k">sub </span><span class="m">srandom ($)</span> <span class="s">{</span>
127 114 <span class="k">my</span><span class="s">(</span><span class="i">$Seed</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
128 115
129 116 <span class="k">if</span> <span class="s">(</span><span class="i">$Seed</span> &lt;= <span class="n">0</span> <span class="s">)</span> <span class="s">{</span>
130 117 <span class="k">die</span> <span class="q">&quot;Error: srandom: Specified seed value must be greater than 0...&quot;</span><span class="sc">;</span>
131 118 <span class="s">}</span>
132 119
133 120 <span class="i">$RandomSeed</span> = <span class="s">(</span><span class="i">$Seed</span> &gt; <span class="i">$MaxRandomSeed</span><span class="s">)</span> ? <span class="s">(</span><span class="i">$Seed</span> % <span class="i">$MaxRandomSeed</span><span class="s">)</span> <span class="co">:</span> <span class="i">$Seed</span><span class="sc">;</span>
134 121
135 122 <span class="k">return</span> <span class="i">$RandomSeed</span><span class="sc">;</span>
136 123 <span class="s">}</span>
137 124
138 125 <span class="c"># Retrun a random number between 0 and less than 1 or specified size...</span>
139 126 <span class="c">#</span>
140 <a name="random-"></a> 127 <span class="k">sub </span><span class="m">random (;$)</span> <span class="s">{</span>
141 128 <span class="k">my</span><span class="s">(</span><span class="i">$Size</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
142 129 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="cm">,</span> <span class="i">$LowValue</span><span class="cm">,</span> <span class="i">$HighValue</span><span class="s">)</span><span class="sc">;</span>
143 130
144 131 <span class="i">$Size</span> = <span class="k">defined</span> <span class="i">$Size</span> ? <span class="i">$Size</span> <span class="co">:</span> <span class="n">1.0</span><span class="sc">;</span>
145 132
146 133 <span class="i">$HighValue</span> = <span class="i">$RandomSeed</span> / <span class="i">$RandomQuotient</span><span class="sc">;</span>
147 134 <span class="i">$LowValue</span> = <span class="i">$RandomSeed</span> % <span class="i">$RandomQuotient</span><span class="sc">;</span>
148 135
149 136 <span class="i">$Value</span> = <span class="i">$RandomMultiplier</span> * <span class="i">$LowValue</span> - <span class="i">$RandomRemainder</span> * <span class="i">$HighValue</span><span class="sc">;</span>
150 137
151 138 <span class="i">$RandomSeed</span> = <span class="s">(</span><span class="i">$Value</span> &gt; <span class="n">0</span><span class="s">)</span> ? <span class="i">$Value</span> <span class="co">:</span> <span class="s">(</span><span class="i">$Value</span> + <span class="i">$RandomModulus</span><span class="s">)</span><span class="sc">;</span>
152 139
153 140 <span class="k">return</span> <span class="s">(</span><span class="i">$RandomSeed</span> / <span class="i">$RandomModulus</span><span class="s">)</span> * <span class="i">$Size</span><span class="sc">;</span>
154 141 <span class="s">}</span>
155 142
156 143 <span class="c"># Round a integer/real number to:</span>
157 144 <span class="c"># . A nearest integer</span>
158 145 <span class="c"># . Specified number of decimal places</span>
159 146 <span class="c">#</span>
160 <a name="round-"></a> 147 <span class="k">sub </span><span class="m">round ($;$)</span> <span class="s">{</span>
161 148 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="cm">,</span> <span class="i">$DecimalPlaces</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
162 149 <span class="k">my</span><span class="s">(</span><span class="i">$RoundedValue</span><span class="s">)</span><span class="sc">;</span>
163 150
164 151 <span class="k">if</span> <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$DecimalPlaces</span><span class="s">)</span> &amp;&amp; <span class="i">$DecimalPlaces</span> &gt; <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
165 152 <span class="i">$RoundedValue</span> = <span class="k">sprintf</span> <span class="q">&quot;%.${DecimalPlaces}f&quot;</span><span class="cm">,</span> <span class="i">$Value</span><span class="sc">;</span>
166 153 <span class="s">}</span>
167 154 <span class="k">else</span> <span class="s">{</span>
168 155 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> &lt; <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
169 156 <span class="i">$RoundedValue</span> = <span class="k">int</span><span class="s">(</span><span class="i">$Value</span> - <span class="n">0.5</span><span class="s">)</span><span class="sc">;</span>
170 157 <span class="s">}</span>
171 158 <span class="k">else</span> <span class="s">{</span>
172 159 <span class="i">$RoundedValue</span> = <span class="k">int</span><span class="s">(</span><span class="i">$Value</span> + <span class="n">0.5</span><span class="s">)</span><span class="sc">;</span>
173 160 <span class="s">}</span>
174 161 <span class="s">}</span>
175 162 <span class="k">return</span> <span class="i">$RoundedValue</span><span class="sc">;</span>
176 163 <span class="s">}</span>
177 164
178 165 <span class="c"># Return tangent of an angle expressed in radians.</span>
179 <a name="tan-"></a> 166 <span class="k">sub </span><span class="m">tan</span> <span class="s">{</span>
180 167 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
181 168
182 169 <span class="k">return</span> <span class="s">(</span><span class="i">CORE::</span><span class="k">sin</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span>/<span class="i">CORE::</span><span class="k">cos</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span>
183 170 <span class="s">}</span>
184 171
185 172 <span class="c"># Return inverse sine of an angle expressed in radians.</span>
186 173 <span class="c">#</span>
187 174 <span class="c"># For a right angle triangle defined by sides X and Y in a unit circle, Pythagorean theorem implies</span>
188 175 <span class="c"># X**2 + Y**2 = 1 and sin value corresponds to Y. So asin is equivalent to atan2(Y, sqrt(1-Y**2)).</span>
189 176 <span class="c"># However, taking sqrt of negative numbers is problematic; Math::Trig::asin handles it using complex</span>
190 177 <span class="c"># numbers.</span>
191 178 <span class="c">#</span>
192 <a name="asin-"></a> 179 <span class="k">sub </span><span class="m">asin ($)</span> <span class="s">{</span>
193 180 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
194 181
195 182 <span class="k">return</span> <span class="i">Math::Trig::asin</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
196 183 <span class="s">}</span>
197 184
198 185 <span class="c"># Return inverse cosine of an angle expressed in radians.</span>
199 186 <span class="c">#</span>
200 187 <span class="c"># For a right angle triangle defined by sides X and Y in a unit circle, Pythagorean theorem implies</span>
201 188 <span class="c"># X**2 + Y**2 = 1 and cos value corresponds to X. So asin is equivalent to atan2(sqrt(1-X**2), X)</span>
202 189 <span class="c"># However, taking sqrt of negative numbers is problematic; Math::Trig::acos handles it using complex</span>
203 190 <span class="c"># numbers.</span>
204 191 <span class="c">#</span>
205 <a name="acos-"></a> 192 <span class="k">sub </span><span class="m">acos ($)</span> <span class="s">{</span>
206 193 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
207 194
208 195 <span class="k">return</span> <span class="i">Math::Trig::acos</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
209 196 <span class="s">}</span>
210 197
211 198 <span class="c"># Generate prime numbers up to a specified limit and return a reference to an</span>
212 199 <span class="c"># array containing the prime numbers.</span>
213 200 <span class="c">#</span>
214 201 <span class="c"># By default, the first 1000 prime numbers are generated. The 1000th prime</span>
215 202 <span class="c"># number is 7919 and that&#39;s why default limit is set to 7920.</span>
216 203 <span class="c">#</span>
217 <a name="GeneratePrimeNumbersUpToLimit-"></a> 204 <span class="k">sub </span><span class="m">GeneratePrimeNumbersUpToLimit (;$)</span> <span class="s">{</span>
218 205 <span class="k">my</span><span class="s">(</span><span class="i">$Limit</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
219 206
220 207 <span class="i">$Limit</span> = <span class="k">defined</span> <span class="i">$Limit</span> ? <span class="i">$Limit</span> <span class="co">:</span> <span class="n">7920</span><span class="sc">;</span>
221 208
222 209 <span class="k">return</span> <span class="i">_GeneratePrimeNumbers</span><span class="s">(</span><span class="q">&#39;ByLimit&#39;</span><span class="cm">,</span> <span class="i">$Limit</span><span class="s">)</span>
223 210 <span class="s">}</span>
224 211
225 212 <span class="c"># Generate prime numbers up to specified count of prime numbers and return a</span>
226 213 <span class="c"># reference to an array containing the prime numbers.</span>
227 214 <span class="c">#</span>
228 215 <span class="c"># By default, the first 1000 prime numbers are generated. The 1000th prime</span>
229 216 <span class="c"># number is 7919.</span>
230 217 <span class="c">#</span>
231 <a name="GeneratePrimeNumbersUpToCount-"></a> 218 <span class="k">sub </span><span class="m">GeneratePrimeNumbersUpToCount (;$)</span> <span class="s">{</span>
232 219 <span class="k">my</span><span class="s">(</span><span class="i">$Count</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
233 220
234 221 <span class="i">$Count</span> = <span class="k">defined</span> <span class="i">$Count</span> ? <span class="i">$Count</span> <span class="co">:</span> <span class="n">1000</span><span class="sc">;</span>
235 222
236 223 <span class="k">return</span> <span class="i">_GeneratePrimeNumbers</span><span class="s">(</span><span class="q">&#39;ByCount&#39;</span><span class="cm">,</span> <span class="i">$Count</span><span class="s">)</span>
237 224 <span class="s">}</span>
238 225
239 226 <span class="c"># Generate prime numbers up to specified limit or count and return a reference</span>
240 227 <span class="c"># to an array containing the prime numbers.</span>
241 228 <span class="c">#</span>
242 229 <span class="c"># The algorithm to generate prime numbers is a modification of Sieve of Erastothenes</span>
243 230 <span class="c"># prime number generator.</span>
244 231 <span class="c">#</span>
245 <a name="_GeneratePrimeNumbers-"></a> 232 <span class="k">sub </span><span class="m">_GeneratePrimeNumbers</span> <span class="s">{</span>
246 233 <span class="k">my</span><span class="s">(</span><span class="i">$Mode</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
247 234 <span class="k">my</span><span class="s">(</span><span class="i">$ByLimit</span><span class="cm">,</span> <span class="i">$PrimeNumber</span><span class="cm">,</span> <span class="i">$Number</span><span class="cm">,</span> <span class="i">$SqrtOfNumber</span><span class="cm">,</span> <span class="i">$NumberIsPrime</span><span class="cm">,</span> <span class="i">@PrimeNumbers</span><span class="s">)</span><span class="sc">;</span>
248 235
249 236 <span class="i">$ByLimit</span> = <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^ByLimit$/i</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span>
250 237
251 238 <span class="i">@PrimeNumbers</span> = <span class="s">(</span><span class="n">2</span><span class="cm">,</span> <span class="n">3</span><span class="s">)</span><span class="sc">;</span>
252 239 <span class="i">$Number</span> = <span class="n">3</span><span class="sc">;</span>
253 240
254 241 <span class="c"># while ($Number &lt;= $Limit) {</span>
255 242 <span class="k">while</span> <span class="s">(</span><span class="i">$ByLimit</span> ? <span class="s">(</span><span class="i">$Number</span> &lt; <span class="i">$Value</span><span class="s">)</span> <span class="co">:</span> <span class="s">(</span><span class="i">@PrimeNumbers</span> &lt; <span class="i">$Value</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
256 243 <span class="i">$Number</span> += <span class="n">2</span><span class="sc">;</span>
257 244 <span class="i">$SqrtOfNumber</span> = <span class="k">sqrt</span> <span class="i">$Number</span><span class="sc">;</span>
258 245
259 246 <span class="i">$NumberIsPrime</span> = <span class="n">1</span><span class="sc">;</span>
260 247 <span class="j">PRIMENUMBER:</span> <span class="k">for</span> <span class="i">$PrimeNumber</span> <span class="s">(</span><span class="i">@PrimeNumbers</span><span class="s">)</span> <span class="s">{</span>
261 248 <span class="k">if</span> <span class="s">(</span><span class="i">$PrimeNumber</span> &gt; <span class="i">$SqrtOfNumber</span><span class="s">)</span> <span class="s">{</span>
262 249 <span class="k">last</span> <span class="j">PRIMENUMBER</span><span class="sc">;</span>
263 250 <span class="s">}</span>
264 251 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$Number</span> % <span class="i">$PrimeNumber</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
265 252 <span class="i">$NumberIsPrime</span> = <span class="n">0</span><span class="sc">;</span>
266 253 <span class="k">last</span> <span class="j">PRIMENUMBER</span><span class="sc">;</span>
267 254 <span class="s">}</span>
268 255 <span class="s">}</span>
269 256 <span class="k">if</span> <span class="s">(</span><span class="i">$NumberIsPrime</span><span class="s">)</span> <span class="s">{</span>
270 257 <span class="k">push</span> <span class="i">@PrimeNumbers</span><span class="cm">,</span> <span class="i">$Number</span><span class="sc">;</span>
271 258 <span class="s">}</span>
272 259 <span class="s">}</span>
273 260 <span class="k">return</span> \<span class="i">@PrimeNumbers</span><span class="sc">;</span>
274 261 <span class="s">}</span>
275 262
276 <a name="EOF-"></a></pre>
277 <p>&nbsp;</p>
278 <br />
279 <center>
280 <img src="../../../images/h2o2.png">
281 </center>
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