A126956 Numbers n such that 3n+2, 4n+3 and 5n+4 are primes.

5, 17, 77, 89, 119, 185, 257, 287, 395, 665, 755, 797, 929, 1175, 1259, 1337, 1379, 1445, 1469, 1769, 2057, 2105, 3125, 3419, 3437, 3629, 3815, 3989, 4079, 4157, 4175, 4217, 4367, 4445, 4847, 5045, 5375, 6089, 6137, 6167, 6359, 6419, 6485, 6725, 6887

Offset: 1

Author

J. M. Bergot, Mar 19 2007

Keywords

• nonn

Examples

			Take n = 185. Then 3*185 + 2 = 557, 4*185 + 3 = 743 and 5*185 + 4 = 929 are primes.
		

Links

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

Crossrefs

Intersection of A024893, A095278, A024897. Cf. A126955.

Programs

Mathematica

Select[Range[7000], PrimeQ[3# + 2] && PrimeQ[4# + 3] && PrimeQ[5# + 4] &] (* Ray Chandler, Mar 20 2007 *)
Select[Range[7000],AllTrue[{3#+2,4#+3,5#+4},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 06 2019 *)

Extensions

Corrected and extended by Ray Chandler, Stuart Clary, Robert G. Wilson v and Zak Seidov, Mar 20 2007