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A174243
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Least of 5 consecutive integers such that their product is the average of a twin prime pair.
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3
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7, 75, 178, 209, 371, 431, 497, 516, 679, 770, 802, 830, 858, 931, 957, 1221, 1232, 1251, 1309, 1397, 1419, 1545, 1567, 1683, 1713, 1714, 1834, 1901, 1991, 2337, 2408, 2441, 2505, 2623, 2651, 2673, 2726, 3142, 3223, 3269, 3349, 3386, 3387, 3461, 3492
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OFFSET
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1,1
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COMMENTS
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7*8*9*10*11=55440 +-1 -> primes,..
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LINKS
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MATHEMATICA
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f1[n_]:=PrimeQ[n-1]&&PrimeQ[n+1]; f2[n_]:=n*(n+1)*(n+2)*(n+3)*(n+4); lst={}; Do[If[f1[f2[n]], AppendTo[lst, n]], {n, 8!}]; lst
Select[Partition[Range[3500], 5, 1], AllTrue[Times@@#+{1, -1}, PrimeQ]&][[All, 1]] (* Harvey P. Dale, May 13 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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