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A203263 Primes p such that 29*p + 14 and 41*p + 20 are also prime.

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%I A203263 #43 Oct 05 2022 17:31:07
%S A203263 61,103,127,271,313,331,373,457,547,571,577,613,877,967,997,1201,1423,
%T A203263 1597,2251,2287,2311,2713,2791,2887,3307,3433,3511,3697,3733,3847,
%U A203263 4261,4327,4363,4483,4861,4951,5023,5407,5563,5743,6553,6571,6781,6991,7177,7333
%N A203263 Primes p such that 29*p + 14 and 41*p + 20 are also prime.
%C A203263 p*(p + 1)/2 is the first number in a set of three triangular numbers with prime indices in arithmetic progression with difference 420*p*(p + 1) + 105. - _Arkadiusz Wesolowski_, Oct 29 2013
%D A203263 Wacław Sierpiński, 200 zadan z elementarnej teorii liczb, Warsaw: PZWS, 1964, pp. 12, 61.
%D A203263 Wacław Sierpiński, 250 Problems in Elementary Number Theory. (Modern Analytic and Computational Methods in Science and Mathematics, No. 26), American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970, pp. 7, 50.
%H A203263 Arkadiusz Wesolowski, <a href="/A203263/b203263.txt">Table of n, a(n) for n = 1..10000</a>
%t A203263 lst = {}; Do[p = Prime[n]; If[PrimeQ[29*p + 14] && PrimeQ[41*p + 20], AppendTo[lst, p]], {n, 10^3}]; lst
%t A203263 Select[Prime[Range[1000]],AllTrue[{29#+14,41#+20},PrimeQ]&] (* _Harvey P. Dale_, Oct 05 2022 *)
%o A203263 (Magma) [p : p in PrimesUpTo(7333) | IsPrime(29*p+14) and IsPrime(41*p+20)]; // _Arkadiusz Wesolowski_, Oct 29 2013
%Y A203263 Cf. A034953.
%K A203263 nonn
%O A203263 1,1
%A A203263 _Arkadiusz Wesolowski_, Jan 13 2012