A050814 Primes p such that inserting any even digit between adjacent digits produces a prime number while inserting any odd digit produces a composite number, or vice versa.

5333, 1454969, 1466833, 1790531, 1794343, 1883113, 1984459, 2179993, 2410523, 2567891, 3100301, 3259567, 3424783, 3700153, 3954131, 3972979, 4046671, 4134133, 4280033, 4544641, 4691851, 4692641, 4848523, 5006831, 5118307

Offset: 1

Author

Patrick De Geest, Oct 15 1999

Keywords

• nonn
• base

Examples

			5333 produces five primes when an even digit is inserted (5030303, 5232323, 5434343, 5636363, 5838383) and five composites when an odd digit is inserted (5131313, 5333333, 5535353, 5737373, 5939393).
		

Crossrefs

Cf. A050674-A050719.

Programs

Mathematica

a[n_,k_]:=Union[Boole/@PrimeQ[Table[FromDigits[Riffle[IntegerDigits[n],i]],{i,k+2*Range[0,4]}]]]; t={}; Do[p=Prime[i]; x=a[p,1]; y=a[p,0]; If[x=={0}&&y=={1}||x=={1}&&y=={0},AppendTo[t,p]],{i,100,190000}]; t (* Jayanta Basu, Jun 01 2013 *)

Extensions

Offset changed to 1 by Jon E. Schoenfield, Oct 17 2019

Name clarified by Tanya Khovanova, Jul 06 2021