Ormiston pairs: Difference between revisions
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=== slower but higher limits === |
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<!--<syntaxhighlight lang="phix">(phixonline)--> |
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<span style="color: #000080;font-style:italic;">-- |
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-- demo\rosetta\Ormiston_pairs.exw |
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-- =============================== |
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-- |
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-- Uses a segmented sieve, which is about half the speed of get_primes_le(), but uses far less memory |
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-- If permited, get_primes_le(1e10) would generate a result of 455,052,511 primes, more than 32 bit |
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-- can cope with, and use over 6GB of ram, and take about 11mins 44s, that is on this box at least, |
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-- whereas this processes them on-the-fly, and only uses about 6MB of memory (ie 0.1% of 6GB). |
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--</span> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span> |
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">ormiston_pairs</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span> |
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<span style="color: #000080;font-style:italic;">// Generate primes using the segmented sieve of Eratosthenes. |
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// credit: https://gist.github.com/kimwalisch/3dc39786fab8d5b34fee</span> |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">segment_size</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)),</span> |
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<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span> |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">low</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span> |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">isprime</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">segment_size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> |
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<span style="color: #000000;">primes</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> |
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<span style="color: #000000;">multiples</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> |
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<span style="color: #000000;">orm30</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)</span> |
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<span style="color: #008080;">while</span> <span style="color: #000000;">low</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">limit</span> <span style="color: #008080;">do</span> |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">sieve</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">segment_size</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">then</span> |
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<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"Processing %,d/%,d (%3.2f%%)\r"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">low</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">low</span><span style="color: #0000FF;">/</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">100</span><span style="color: #0000FF;">})</span> |
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<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000080;font-style:italic;">// current segment = [low, high]</span> |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">high</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">low</span><span style="color: #0000FF;">+</span><span style="color: #000000;">segment_size</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)</span> |
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<span style="color: #000080;font-style:italic;">// generate sieving primes using simple sieve of Eratosthenes</span> |
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<span style="color: #008080;">while</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">high</span><span style="color: #0000FF;">,</span><span style="color: #000000;">segment_size</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">isprime</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">i</span> <span style="color: #008080;">to</span> <span style="color: #000000;">segment_size</span> <span style="color: #008080;">by</span> <span style="color: #000000;">i</span> <span style="color: #008080;">do</span> |
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<span style="color: #000000;">isprime</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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<span style="color: #000080;font-style:italic;">// initialize sieving primes for segmented sieve</span> |
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<span style="color: #008080;">while</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">high</span> <span style="color: #008080;">do</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">isprime</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> |
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<span style="color: #000000;">primes</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">s</span> |
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<span style="color: #000000;">multiples</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">-</span><span style="color: #000000;">low</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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<span style="color: #000080;font-style:italic;">// sieve the current segment</span> |
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<span style="color: #008080;">for</span> <span style="color: #000000;">mi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span> <span style="color: #008080;">in</span> <span style="color: #000000;">multiples</span> <span style="color: #008080;">do</span> |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">primes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mi</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">2</span> |
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<span style="color: #008080;">while</span> <span style="color: #000000;">j</span><span style="color: #0000FF;"><</span><span style="color: #000000;">segment_size</span> <span style="color: #008080;">do</span> |
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<span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> |
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<span style="color: #000000;">j</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">k</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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<span style="color: #000000;">multiples</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mi</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">segment_size</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<span style="color: #008080;">while</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">high</span> <span style="color: #008080;">do</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">low</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: #000080;font-style:italic;">// n is a prime</span> |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">18</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> |
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<span style="color: #008080;">and</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">))=</span><span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">then</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">p1</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">nc</span> <span style="color: #008080;">then</span> |
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<span style="color: #004080;">string</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">elapsed_short</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span> |
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<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%,d Ormiston pairs before %,d (%s)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nc</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">})</span> |
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<span style="color: #000000;">nc</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">30</span> <span style="color: #008080;">then</span> |
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<span style="color: #000000;">orm30</span><span style="color: #0000FF;">[</span><span style="color: #000000;">count</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"[%5d %5d]"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">})</span> |
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<span style="color: #008080;">if</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">=</span><span style="color: #000000;">30</span> <span style="color: #008080;">then</span> |
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<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;">"First 30 Ormiston pairs:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">orm30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">))</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">2</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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<span style="color: #000000;">low</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">segment_size</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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<span style="color: #004080;">string</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">elapsed_short</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span> |
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<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%,d Ormiston pairs before %,d (%s)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nc</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">})</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
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<span style="color: #000000;">ormiston_pairs</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span><span style="color: #0000FF;">?</span><span style="color: #000000;">1e8</span><span style="color: #0000FF;">:</span><span style="color: #000000;">1e10</span><span style="color: #0000FF;">))</span> |
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<!--</syntaxhighlight>--> |
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{{out}} |
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With limit upped to 1e10 |
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<pre> |
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First 30 Ormiston pairs: |
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[ 1913 1931] [18379 18397] [19013 19031] |
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[25013 25031] [34613 34631] [35617 35671] |
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[35879 35897] [36979 36997] [37379 37397] |
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[37813 37831] [40013 40031] [40213 40231] |
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[40639 40693] [45613 45631] [48091 48109] |
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[49279 49297] [51613 51631] [55313 55331] |
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[56179 56197] [56713 56731] [58613 58631] |
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[63079 63097] [63179 63197] [64091 64109] |
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[65479 65497] [66413 66431] [74779 74797] |
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[75913 75931] [76213 76231] [76579 76597] |
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40 Ormiston pairs before 100,000 (0s) |
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382 Ormiston pairs before 1,000,000 (0s) |
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3,722 Ormiston pairs before 10,000,000 (0s) |
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34,901 Ormiston pairs before 100,000,000 (5s) |
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326,926 Ormiston pairs before 1,000,000,000 (55s) |
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3,037,903 Ormiston pairs before 10,000,000,000 (21:57) |
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</pre> |
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Note that running this under pwa/p2js with a limit of 1e9 would get you a blank screen for 1min 25s, hence I've limited it to 1e8 (8s)<br> |
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I have not the patience to see whether JavaScript would actually cope with 1e10, but it should (with a blank screen for at least half an hour). |
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=={{header|Python}}== |
=={{header|Python}}== |