Sexy primes: Difference between revisions
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m (Changed step to "2 * p" instead of "p" in sieve of Erathostenes.) |
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1 quintuplets, ending with: (5 11 17 23 29) |
1 quintuplets, ending with: (5 11 17 23 29) |
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48627 unsexy, ending with: 999853 999863 999883 999907 999917 999931 999961 999979 999983 1000003</pre> |
48627 unsexy, ending with: 999853 999863 999883 999907 999917 999931 999961 999979 999983 1000003</pre> |
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=={{header|Mathematica}} / {{header|Wolfram Language}}== |
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<lang Mathematica>ClearAll[AllSublengths] |
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AllSublengths[l_List] := If[Length[l] > 2, |
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Catenate[Partition[l, #, 1] & /@ Range[2, Length[l]]] |
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, |
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{l} |
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] |
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primes = Prime[Range[PrimePi[1000035]]]; |
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ps = Union[Intersection[primes + 6, primes] - 6, Intersection[primes - 6, primes] + 6]; |
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a = Intersection[ps + 6, ps] - 6; |
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b = Intersection[ps - 6, ps] + 6; |
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g = Graph[DeleteDuplicates[Thread[a \[UndirectedEdge] (a + 6)]~Join~Thread[(b - 6) \[UndirectedEdge] b]]]; |
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sp = Sort /@ ConnectedComponents[g]; |
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sp //= SortBy[First]; |
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sp //= Map[AllSublengths]; |
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sp //= Catenate; |
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sp //= SortBy[First]; |
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sp //= DeleteDuplicates; |
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sel = Select[sp, Length /* EqualTo[2]]; |
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Length[sel] |
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sel[[-5 ;;]] // Column |
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sel = Select[sp, Length /* EqualTo[3]]; |
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Length[sel] |
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sel[[-5 ;;]] // Column |
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sel = Select[sp, Length /* EqualTo[4]]; |
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Length[sel] |
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sel[[-5 ;;]] // Column |
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sel = Select[sp, Length /* EqualTo[5]]; |
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Length[sel] |
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sel // Column |
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Select[Complement[primes, DeleteDuplicates[Catenate@sp]][[-20 ;;]], ! (PrimeQ[# + 6] \[Or] PrimeQ[# - 6]) &][[-10 ;;]] // Column</lang> |
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{{out}} |
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<pre>16386 |
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{999371,999377} |
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{999431,999437} |
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{999721,999727} |
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{999763,999769} |
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{999953,999959} |
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2900 |
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{997427,997433,997439} |
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{997541,997547,997553} |
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{998071,998077,998083} |
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{998617,998623,998629} |
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{998737,998743,998749} |
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325 |
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{977351,977357,977363,977369} |
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{983771,983777,983783,983789} |
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{986131,986137,986143,986149} |
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{990371,990377,990383,990389} |
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{997091,997097,997103,997109} |
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1 |
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{5,11,17,23,29} |
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999853 |
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999863 |
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999883 |
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999907 |
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999917 |
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999931 |
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999961 |
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999979 |
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999983 |
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1000003</pre> |
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=={{header|Nim}}== |
=={{header|Nim}}== |