A274527 Prime numbers p such that p+2, p^2+p-1, p^2+p+1, p^2+3*p+1, p^2+3*p+3 are all prime numbers.

5, 2729, 26449079, 27188279, 44521679, 46090379, 52736249, 62320439, 70777979, 92520539, 109505969, 192153149, 274448789, 288269519, 343801919, 359240069, 515694899, 521594639, 527159429, 660223409, 809600819, 857353139, 921868289, 945420629, 1000777049

Offset: 1

Author

Pierre CAMI, Jun 27 2016

Keywords

• nonn

Examples

			2 first prime, 2+2=4 composite.
3 prime, 3+2=5 prime, 3^2+3-1=11 prime, 3^2+3+1=13 prime, 3^2+3*3+1=19 prime, 3^2+3*3+3=21 composite.
5 prime, 5+2=7 prime, 5^2+5-1=29 prime, 5^2+5+1=31 prime, 5^2+3*5+1=41 prime, 5^2+3*5+3=43 prime so a(1)=5
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..45

Crossrefs

Cf. A228968, A274525.

Programs

Mathematica

Select[Prime[Range[50890000]],AllTrue[{#+2,#^2+#-1,#^2+#+1,#^2+3#+1,#^2+3#+3},PrimeQ]&] (* Harvey P. Dale, Aug 13 2021 *)