A128548 Primes p such that p*q-p-q and p*q+p+q are prime where q=nextprime(p).

3, 5, 13, 43, 89, 163, 479, 643, 683, 773, 811, 953, 1109, 1399, 1471, 2213, 2741, 3253, 4583, 5153, 5923, 6427, 7649, 9059, 10151, 10531, 12301, 12373, 13553, 13903, 13921, 14723, 14869, 14929, 16183, 17123, 17681, 21149, 21377, 21569, 21587

Offset: 1

Author

Zak Seidov, Mar 10 2007

Keywords

• nonn
• changed

Comments

Intersection of A126148 and A128546.

Examples

			3*5-3-5=7 and 3*5+3+5=23 are prime, 5*7-5-23=7 and 5*7+5+7=47 are primes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096342, A126148, A128547.

Programs

Mathematica

Select[Partition[Prime[Range[2500]],2,1],AllTrue[Times@@#+{Total[#],-Total[#]},PrimeQ]&][[;;,1]] (* Harvey P. Dale, Aug 30 2025 *)

PARI

isok(p) = isprime(p) && (q = nextprime(p+1)) && isprime(p*q-p-q) && isprime(p*q+p+q); \\ Michel Marcus, Oct 11 2013