Prime numbers whose neighboring pairs are tetraprimes: Difference between revisions
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Added XPL0 example. |
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Median gap between those 10,551 primes : 660 |
Median gap between those 10,551 primes : 660 |
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Maximum gap between those 10,551 primes : 10,284 |
Maximum gap between those 10,551 primes : 10,284 |
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</pre> |
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=={{header|XPL0}}== |
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<syntaxhighlight lang "XPL0">include xpllib; \for Print |
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int Have7; \A tetraprime factor is 7 |
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proc IsTetraprime(N); \Return 'true' if N is a tetraprime |
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int N; |
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int Div, Count, Distinct; |
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[Div:= 2; Count:= 0; |
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while N >= Div*Div do |
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[Distinct:= true; |
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while rem(N/Div) = 0 do |
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[if not Distinct then return false; |
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Distinct:= false; |
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Count:= Count+1; |
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if Div = 7 then Have7:= true; |
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N:= N/Div; |
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]; |
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Div:= Div+1; |
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]; |
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if N > 1 then Count:= Count+1; |
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return Count = 4; |
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]; |
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int Sign, TenPower, TP, Case, N, N0, Count, Count7, Gap, GapMin, GapMax, GapSum; |
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[Sign:= -1; TenPower:= 100_000; |
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for TP:= 5 to 7 do |
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[for Case:= 1 to 2 do \preceding or following neighboring pairs |
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[Count:= 0; Count7:= 0; N0:= 0; GapMin:= -1>>1; GapMax:= 0; GapSum:= 0; |
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if TP = 5 then CrLf(0); \100_000 |
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for N:= 3 to TenPower-1 do |
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[if IsPrime(N) then |
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[Have7:= false; |
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if IsTetraprime(N+1*Sign) then |
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if IsTetraprime(N+2*Sign) then |
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[Count:= Count+1; |
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if TP = 5 then |
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[Print("%7d", N); |
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if rem(Count/10) = 0 then CrLf(0); |
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]; |
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if Have7 then Count7:= Count7+1; |
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if N0 # 0 then |
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[Gap:= N - N0; |
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if Gap < GapMin then GapMin:= Gap; |
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if Gap > GapMax then GapMax:= Gap; |
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GapSum:= GapSum + Gap; |
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]; |
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N0:= N; |
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]; |
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]; |
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N:= N+1; |
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]; |
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Print("\nFound %,d primes under %,d whose neighboring pair are tetraprimes\n", |
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Count, TenPower); |
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Print("of which %,d have a neighboring pair, one of whose factors is 7.\n\n", |
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Count7); |
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Print("Minimum gap between %d primes : %,d\n", Count, GapMin); |
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Print("Average gap between %d primes : %,d\n", Count, |
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fix(float(GapSum)/float(Count-1))); |
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Print("Maximum gap between %d primes : %,d\n", Count, GapMax); |
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Sign:= Sign * -1; |
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]; |
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TenPower:= TenPower * 10; |
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]; |
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]</syntaxhighlight> |
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{{out}} |
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<pre> |
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8647 15107 20407 20771 21491 23003 23531 24767 24971 27967 |
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29147 33287 34847 36779 42187 42407 42667 43331 43991 46807 |
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46867 51431 52691 52747 53891 54167 58567 63247 63367 69379 |
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71711 73607 73867 74167 76507 76631 76847 80447 83591 84247 |
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86243 87187 87803 89387 93887 97547 97847 98347 99431 |
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Found 49 primes under 100,000 whose neighboring pair are tetraprimes |
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of which 31 have a neighboring pair, one of whose factors is 7. |
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Minimum gap between 49 primes : 56 |
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Average gap between 49 primes : 1,891 |
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Maximum gap between 49 primes : 6,460 |
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8293 16553 17389 18289 22153 26893 29209 33409 35509 36293 |
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39233 39829 40493 41809 45589 48109 58393 59629 59753 59981 |
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60493 60913 64013 64921 65713 66169 69221 71329 74093 75577 |
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75853 77689 77933 79393 79609 82913 84533 85853 87589 87701 |
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88681 91153 93889 96017 97381 98453 |
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Found 46 primes under 100,000 whose neighboring pair are tetraprimes |
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of which 36 have a neighboring pair, one of whose factors is 7. |
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Minimum gap between 46 primes : 112 |
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Average gap between 46 primes : 2,004 |
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Maximum gap between 46 primes : 10,284 |
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Found 885 primes under 1,000,000 whose neighboring pair are tetraprimes |
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of which 503 have a neighboring pair, one of whose factors is 7. |
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Minimum gap between 885 primes : 4 |
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Average gap between 885 primes : 1,119 |
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Maximum gap between 885 primes : 7,712 |
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Found 866 primes under 1,000,000 whose neighboring pair are tetraprimes |
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of which 492 have a neighboring pair, one of whose factors is 7. |
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Minimum gap between 866 primes : 4 |
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Average gap between 866 primes : 1,146 |
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Maximum gap between 866 primes : 10,284 |
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Found 10,815 primes under 10,000,000 whose neighboring pair are tetraprimes |
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of which 5,176 have a neighboring pair, one of whose factors is 7. |
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Minimum gap between 10815 primes : 4 |
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Average gap between 10815 primes : 924 |
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Maximum gap between 10815 primes : 9,352 |
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Found 10,551 primes under 10,000,000 whose neighboring pair are tetraprimes |
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of which 5,069 have a neighboring pair, one of whose factors is 7. |
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Minimum gap between 10551 primes : 4 |
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Average gap between 10551 primes : 947 |
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Maximum gap between 10551 primes : 10,284 |
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</pre> |
</pre> |