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Primes p such that 2*q+3 = p^2, where q is prime.
8

%I #16 Sep 08 2022 08:45:20

%S 3,5,7,11,13,19,23,29,31,37,41,47,67,73,79,97,101,103,109,151,157,197,

%T 211,227,233,239,257,263,293,307,331,337,349,353,359,367,389,397,409,

%U 443,449,463,487,491,509,521,547,569,571,587,613,619,653,661,673,727

%N Primes p such that 2*q+3 = p^2, where q is prime.

%H Amiram Eldar, <a href="/A110589/b110589.txt">Table of n, a(n) for n = 1..10000</a>

%p ispower := proc(n,b) andmap(proc(w) evalb(w[2] mod b = 0) end, ifactors(n)[2]) end: a:=2: SQRTP||a:=[]; for z from 1 to 1 do for n from 1 to 10000 do p:=ithprime(n); m:=a*p+a+1; if ispower(m,2) and isprime(sqrt(m)) then SQRTP||a:=[op(SQRTP||a),sqrt(m)] fi od; od; SQRTP||a;

%t fQ[n_] := PrimeQ[(n^2 - 3)/2]; Select[ Prime@ Range@129, fQ@# &] (* _Robert G. Wilson v_, Jun 19 2006 *)

%t Select[Table[Sqrt[2 Prime[n] + 3], {n, 1, 30000}], PrimeQ] (* _Vincenzo Librandi_, Mar 19 2015 *)

%o (Magma) [p: p in PrimesUpTo(1000) | IsPrime((p^2-3) div 2)]; // _Vincenzo Librandi_, Mar 19 2015

%Y Cf. A098828, A109358.

%K nonn

%O 1,1

%A _Walter Kehowski_, Sep 13 2005

%E More terms from _Robert G. Wilson v_, Jun 19 2006