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How do I print only the values of p which are all True?

In addition, is this an efficient use of a Loop in this situation or can this be improved without using a lietral for loop?

For[i = 10200, i <= 10500, i++, v = Divisors[i]; p = PrimeQ[v + (i/v)]; Print[i]; Print[p]]

Thanks.

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Clear["Global`*"]; test[i_] := AllTrue[Divisors[i], PrimeQ[# + (i/#)] &]; Select[Range[10200, 10500], test] (* {10222, 10390, 10462} *)
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