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ClearAll[FindUltraUsefulPrimeK]
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FindUltraUsefulPrimeK[n_] := Module[{num, tmp},
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num = 2^(2^n);
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Do[
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If[PrimeQ[num - k],
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tmp = k;
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Break[];
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]
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,
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{k, 1, \[Infinity], 2}
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];
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tmp
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]
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res = FindUltraUsefulPrimeK /@ Range[13];
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TableForm[res, TableHeadings -> Automatic]
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