A176619 Primes p such that 2p + 3, 4p + 9, 3p + 2 and 9p + 8 are also primes.

5, 7, 97, 167, 397, 607, 2617, 2707, 7687, 12097, 14407, 16787, 19577, 22307, 23827, 24967, 25717, 28547, 31687, 43037, 43517, 46817, 58967, 59617, 63607, 70237, 70957, 78517, 85027, 96797

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 22 2010

Keywords

• nonn

Comments

These primes stay prime under two iterations of p->2p+3 as well as under two iterations of p->3p+2.

For all entries >5 the least significant digit is 7.

Examples

			2*5 + 3 = 13 = prime(6),
4*5 + 9 = 29 = prime(10),
3*5 + 2 = 17 = prime(7),
9*5 + 8 = 53 = prime(16); 5 = prime(3) = a(1).
		

References

• Joe Buhler: Algorithmic Number Theory: Third International Symposium, ANTS-III, Springer New York, 1998
• F. Ischebeck: Einladung zur Zahlentheorie, B. I. Wissenschaftsverlag, Mannheim-Leipzig-Wien-Zuerich, 1992

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A005602, A023242, A023246, A059762.

Programs

Magma

[p: p in PrimesUpTo(100000)|IsPrime(2*p+3) and IsPrime(4*p+9) and IsPrime(3*p+2) and IsPrime(9*p+8 )] // Vincenzo Librandi, Jan 29 2011

Mathematica

Select[Prime[Range[10000]],AllTrue[{2#+3,4#+9,3#+2,9#+8},PrimeQ]&] (* Harvey P. Dale, Dec 15 2024 *)

Formula

A023242 INTERSECT A023246.