A178084 Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes.

1, 10, 148, 1606, 1942, 2101, 2227, 4378, 5533, 14416, 16570, 16684, 19573, 20182, 22534, 24760, 26881, 32614, 34798, 36121, 39775, 46516, 51880, 53644, 63346, 63379, 66109, 76819, 79579, 82972, 85795, 87601, 95854, 100885, 102250, 106396

Offset: 1

Author

Roger L. Bagula, May 19 2010

Keywords

• nonn

Comments

These primes sets are just like 3k-4 and 3k-2 (or 6k-1 and 6*k+1) prime pairs, only five in a row.

Examples

			k =    1:    11,    13,    17,    19,    23,
k =   10:   101,   103,   107,   109,   113,
k =  148:  1481,  1483,  1487,  1489,  1493,
k = 1606: 16061, 16063, 16067, 16069, 16073,
k = 1942: 19421, 19423, 19427, 19429, 19433,
k = 2101: 21011, 21013, 21017, 21019, 21023,
k = 2227: 22271, 22273, 22277, 22279, 22283
		

Links

• Aaron Toponce, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007811.

Programs

Magma

[n: n in [0..1000]| IsPrime(10*n+1) and IsPrime(10*n+3) and IsPrime(10*n+7) and IsPrime(10*n+9) and IsPrime(10*n+13)] // Vincenzo Librandi, Nov 30 2010

Mathematica

Flatten[Table[If[PrimeQ[10* n + 1] && PrimeQ[10*n + 3] && PrimeQ[10*n + 7] && PrimeQ[10*n + 9] && PrimeQ[10*(n + 1) + 3], n, {}], {n, 0, 50000}]]

Extensions

More terms from Vincenzo Librandi, May 23 2010