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A306931
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Primes p of the form 8*k + 3 such that every prime divisor of p-2 has the form 8*t + 7.
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3
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163, 331, 499, 1171, 1459, 2179, 2203, 2371, 2683, 3019, 5179, 5923, 6043, 6211, 6379, 6883, 7219, 7411, 7723, 8059, 8443, 8563, 9643, 10099, 10651, 10723, 11083, 11131, 11251, 12739, 12763, 13099, 13963, 14779, 14851, 15091, 15451, 16963, 17203
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listen;
history;
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internal format)
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OFFSET
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1,1
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REFERENCES
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L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 476.
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LINKS
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MAPLE
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with(numtheory);
s:=[];
for n from 3 to 5000 do
p:=ithprime(n); p2:=((p+16) mod 8);
if (p2=3) then sw:=1;
for q in factorset(p-2) do if (q mod 8) <> 7 then sw:=-1; break; fi; od:
if sw=1 then s:=[op(s), p]; fi;
fi;
od:
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MATHEMATICA
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Select[8*Range[0, 2500] + 3, PrimeQ[#] && AllTrue[FactorInteger[# - 2][[;; , 1]], Mod[#1, 8] == 7 &] &] (* Amiram Eldar, Dec 05 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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