A050805 Inserting any digit between adjacent digits of prime p never yields another prime.

439, 853, 1013, 1061, 1109, 1117, 1153, 1187, 1213, 1249, 1259, 1283, 1291, 1301, 1303, 1361, 1427, 1451, 1489, 1511, 1523, 1531, 1583, 1597, 1607, 1657, 1733, 1747, 1753, 1801, 1873, 1879, 1913, 1951, 2069, 2083, 2137, 2243, 2251, 2267, 2293, 2297

Offset: 1

Author

Patrick De Geest, Oct 15 1999

Keywords

• nonn
• nice
• base

Examples

			40309, 41319, 42327, 43339, 44349, 45359, 46369, 47379, 48389, and 49399 are all composite. Thus, 439, being prime, belongs to the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050674-A050719, A050806.

Cf. A010051, A000040.

Programs

Haskell

import Data.List (intersperse)
a050805 n = a050805_list !! (n-1)
a050805_list = filter ((all (== 0)) . f) a000040_list where
   f p = map (i $ show p) "0123456789"
   i ps d = a010051' (read $ intersperse d ps :: Integer)
-- Reinhard Zumkeller, May 07 2013

Mathematica

a[n_]:=Or@@PrimeQ[Table[FromDigits[Riffle[IntegerDigits[n],k]],{k,0,9}]]; Select[Prime[Range[5,350]],a[#]==False&] (* Jayanta Basu, May 30 2013 *)
Select[Prime[Range[400]],NoneTrue[Table[FromDigits[Riffle[ IntegerDigits[ #],d]],{d,0,9}],PrimeQ]&] (* Harvey P. Dale, Aug 04 2021 *)

Extensions

Offset corrected by Reinhard Zumkeller, May 07 2013