A243528 Integers n such that p = 4n + 1, q = 4p + 3, r = 4q + 5, s = 4r + 7 and t = 4s + 9 are all prime.

1564, 4057, 4654, 5884, 26599, 30139, 37204, 66532, 74227, 80812, 98137, 113929, 124249, 138604, 245524, 249847, 250879, 299767, 309469, 315277, 340504, 346279, 359467, 362674, 367069, 401407, 410332, 435049, 437377, 438799, 537844, 550582, 579814, 587047

Offset: 1

Author

Zak Seidov, Jun 06 2014

Keywords

• nonn

Comments

The first prime n is 4057.

Examples

			First 3 values of n, p, q, r, s and t:
{1564, 6257, 25031, 100129, 400523, 1602101},
{4057, 16229, 64919, 259681, 1038731, 4154933},
{4654, 18617, 74471, 297889, 1191563, 4766261}.
		

Links

• Zak Seidov, Table of first 30 values of n, p, q, r, s, t.

Programs

Magma

A141291:=func; [n: n in [1..10^6] | forall{i: i in [1..5] | IsPrime(4^i*n + A141291(i))}]; // Bruno Berselli, Jun 06 2014

Mathematica

pqrstQ[n_]:=Module[{p=4n+1,q,r,s},q=4p+3;r=4q+5;s=4r+7;AllTrue[{p,q,r,s,4s+9},PrimeQ]]; Select[Range[590000],pqrstQ] (* Harvey P. Dale, Jan 18 2024 *)