Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,73 +1,71 @@
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(phixonline)-->
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<span style="color: #008080;">function</span> <span style="color: #000000;">create_sieve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">limit</span><span style="color: #0000FF;">)</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;">limit</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">sieve</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;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">4</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</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;">i</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;">for</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</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> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">p</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;">p2</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;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">p2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">by</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</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;">k</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: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">sieve</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function create_sieve(integer limit)
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sequence sieve = repeat(true,limit)
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sieve[1] = false
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for i=4 to limit by 2 do
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sieve[i] = false
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end for
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for p=3 to floor(sqrt(limit)) by 2 do
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integer p2 = p*p
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if sieve[p2] then
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for k=p2 to limit by p*2 do
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sieve[k] = false
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end for
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end if
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end for
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return sieve
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end function
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<span style="color: #008080;">constant</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1000035</span><span style="color: #0000FF;">,</span>
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<span style="color: #000080;font-style:italic;">--constant lim = 100, -- (this works too)</span>
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<span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lim</span><span style="color: #0000FF;">-(</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (limit must be odd)</span>
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<span style="color: #000000;">sieve</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">create_sieve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">+</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (+6 to check for sexiness)</span>
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constant lim = 1000035,
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--constant lim = 100, -- (this works too)
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limit = lim-(and_bits(lim,1)=0), -- (limit must be odd)
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sieve = create_sieve(limit+6) -- (+6 to check for sexiness)
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">sets</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">5</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (unsexy,pairs,trips,quads,quins)</span>
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<span style="color: #000000;">limits</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</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;">counts</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</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;">4</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (2 is an unsexy prime)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- ""</span>
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sequence sets = repeat({},5), -- (unsexy,pairs,trips,quads,quins)
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limits = {10,5,4,3,1},
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counts = 1&repeat(0,4) -- (2 is an unsexy prime)
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integer total = 1 -- ""
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">limit</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (this loop skips 2)</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;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">total</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;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]=</span><span style="color: #004600;">false</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">6</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]=</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">counts</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: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- unsexy</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">limits</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;">sets</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: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">i</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;">else</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">}</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;">6</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">j</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <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: #004600;">false</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">limits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">],</span><span style="color: #000000;">set</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: #000000;">counts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]</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;">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: #008080;">end</span> <span style="color: #008080;">if</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;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])<</span><span style="color: #000000;">limits</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;">sets</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: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</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: #000080;font-style:italic;">-- (as 2 skipped above)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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for i=limit to 3 by -2 do -- (this loop skips 2)
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if sieve[i] then
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total += 1
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if sieve[i+6]=false and (i-6<0 or sieve[i-6]=false) then
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counts[1] += 1 -- unsexy
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if length(sets[1])<limits[1] then
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sets[1] = prepend(sets[1],i)
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end if
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else
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sequence set = {i}
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for j=i-6 to 3 by -6 do
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if j<=0 or sieve[j]=false then exit end if
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set = prepend(set,j)
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integer l = length(set)
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if length(sets[l])<limits[l] then
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sets[l] = prepend(sets[l],set)
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end if
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counts[l] += 1
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end for
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end if
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end if
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end for
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if length(sets[1])<limits[1] then
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sets[1] = prepend(sets[1],2) -- (as 2 skipped above)
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end if
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<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
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Of %,d primes less than %,d there are:
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%,d unsexy primes, the last %d being %s
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%,d pairs, the last %d being %s
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%,d triplets, the last %d being %s
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%,d quadruplets, the last %d being %s
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%,d quintuplet, the last %d being %s
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"""</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">results</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">total</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">,</span>
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<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: #008000;">""</span><span style="color: #0000FF;">,</span>
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<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: #008000;">""</span><span style="color: #0000FF;">,</span>
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<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: #008000;">""</span><span style="color: #0000FF;">,</span>
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<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: #008000;">""</span><span style="color: #0000FF;">,</span>
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<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: #008000;">""</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">results</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;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">3</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">counts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]),</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sets</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])}</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">results</span><span style="color: #0000FF;">)</span>
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<!--
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constant fmt = """
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Of %,d primes less than %,d there are:
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%,d unsexy primes, the last %d being %s
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%,d pairs, the last %d being %s
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%,d triplets, the last %d being %s
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%,d quadruplets, the last %d being %s
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%,d quintuplet, the last %d being %s
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"""
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sequence results = {total,lim,
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0,0,"",
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0,0,"",
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0,0,"",
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0,0,"",
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0,0,""}
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for i=1 to 5 do
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results[i*3..i*3+2] = {counts[i],length(sets[i]),sprint(sets[i])}
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end for
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printf(1,fmt,results)
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