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Reduced tests to 23
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;Advanced:
Solve by testing at most 3123 numbers for primality. Show a list of all numbers tested that were not prime.
<br><br>
 
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=={{header|Phix}}==
There is no need for a limit of 500. This tests a total of just 3123 numbers for primality.
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">a085823</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">={},</span> <span style="color: #000000;">tested</span><span style="color: #0000FF;">={},</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style!="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100p</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1110</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tested</span><span style="color: #0000FF;">}t</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">a085823p</span><span style="color: #0000FF;">(*</span><span style="color: #000000;">res</span><span style="color: #0000FF;">&</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tested</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)10</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">else</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tested</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a085823</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">&</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tested</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">tested</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">t</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<pre>
There are 9 such A085823 primes: {2,23,3,37,373,5,53,7,73}
2214 innocent bystanders falsly accused of being prime (3123 tests in total):
{233,235,237,25,27,33,35,3733,3735,3737,375,377,533,535,537,55,57,733,735,737,75,77}
</pre>