Prime numbers whose neighboring pairs are tetraprimes: Difference between revisions

=={{header|Phix}}==

{{trans|Wren}}

<!--<syntaxhighlight lang="phix">(phixonline)-->

<span style="color: #008080;">constant</span> <span style="color: #000000;">primes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1e7</span><span style="color: #0000FF;">)</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">tetras</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{},{}},</span>

<span style="color: #000000;">sevens</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>

<span style="color: #000000;">highs</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1e5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1e6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1e7</span><span style="color: #0000FF;">},</span>

<span style="color: #000000;">highdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">binary_search</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">highs</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">}}),</span>

<span style="color: #000000;">highest</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">extract</span><span style="color: #0000FF;">(</span><span style="color: #000000;">primes</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">highdx</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">hdx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>

<span style="color: #008080;">for</span> <span style="color: #000000;">p</span> <span style="color: #008080;">in</span> <span style="color: #000000;">primes</span> <span style="color: #008080;">from</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>

<span style="color: #000080;font-style:italic;">-- for all odd primes, both p-1 and p+1 are divisible by 2.

-- one of them will be divisible by 4 and hence not a tetraprime.</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">odd</span><span style="color: #0000FF;">((</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>

<span style="color: #000000;">dx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">?-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">:+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">f3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prime_powers</span><span style="color: #0000FF;">((</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f3</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">3</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">f4</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prime_powers</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dx</span><span style="color: #0000FF;">)</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f4</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">4</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span>

<span style="color: #000000;">tetras</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">d</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">p</span>

<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>

<span style="color: #008080;">or</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">then</span>

<span style="color: #000000;">sevens</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">d</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</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;">if</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">highest</span><span style="color: #0000FF;">[</span><span style="color: #000000;">hdx</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>

<span style="color: #008080;">for</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ti</span> <span style="color: #008080;">in</span> <span style="color: #000000;">tetras</span> <span style="color: #008080;">do</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">)</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Found %,d primes under %,d whose %sing neighboring pair are tetraprimes%s\n"</span><span style="color: #0000FF;">,</span>

<span style="color: #0000FF;">{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">highs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">hdx</span><span style="color: #0000FF;">],</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"preced"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"follow"</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">t</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hdx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">":"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)})</span>

<span style="color: #008080;">if</span> <span style="color: #000000;">hdx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%5d"</span><span style="color: #0000FF;">)})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"of which %,d have a neighboring pair one of whose factors is 7.\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sevens</span><span style="color: #0000FF;">[</span><span style="color: #000000;">t</span><span style="color: #0000FF;">])</span>

<span style="color: #004080;">sequence</span> <span style="color: #000000;">gaps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]))</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Minimum gap between those %,d primes : %,d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gaps</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]})</span>

<span style="color: #000080;font-style:italic;">-- printf(1,"Average gap between those %,d primes : %,d\n",{c,average(gaps)})</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Median gap between those %,d primes : %,d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">median</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gaps</span><span style="color: #0000FF;">)})</span>

<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Maximum gap between those %,d primes : %,d\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gaps</span><span style="color: #0000FF;">[$]})</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>

<span style="color: #000000;">hdx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</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>

<!--</syntaxhighlight>-->

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