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

61, 103, 127, 271, 313, 331, 373, 457, 547, 571, 577, 613, 877, 967, 997, 1201, 1423, 1597, 2251, 2287, 2311, 2713, 2791, 2887, 3307, 3433, 3511, 3697, 3733, 3847, 4261, 4327, 4363, 4483, 4861, 4951, 5023, 5407, 5563, 5743, 6553, 6571, 6781, 6991, 7177, 7333

Offset: 1

Author

Arkadiusz Wesolowski, Jan 13 2012

Keywords

• nonn

Comments

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

References

• Wacław Sierpiński, 200 zadan z elementarnej teorii liczb, Warsaw: PZWS, 1964, pp. 12, 61.
• 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.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034953.

Programs

Magma

[p : p in PrimesUpTo(7333) | IsPrime(29*p+14) and IsPrime(41*p+20)]; // Arkadiusz Wesolowski, Oct 29 2013

Mathematica

lst = {}; Do[p = Prime[n]; If[PrimeQ[29*p + 14] && PrimeQ[41*p + 20], AppendTo[lst, p]], {n, 10^3}]; lst
Select[Prime[Range[1000]],AllTrue[{29#+14,41#+20},PrimeQ]&] (* Harvey P. Dale, Oct 05 2022 *)