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

1,2

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.

Links

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

Example

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

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}]]

Prog

(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

Crossrefs

Cf. A007811.

Sequence in context: A295524 A095889 A097638 * A098270 A262738 A271467

Adjacent sequences: A178081 A178082 A178083 * A178085 A178086 A178087

Keyword

nonn

Author

Roger L. Bagula, May 19 2010

Extensions

More terms from Vincenzo Librandi, May 23 2010

Status

approved