A069489 Primes > 1000 in which every substring of length 3 is also prime.

1013, 1019, 1031, 1097, 1277, 1373, 1499, 1571, 1733, 1811, 1997, 2113, 2239, 2293, 2719, 3079, 3137, 3313, 3373, 3491, 3499, 3593, 3673, 3677, 3733, 3739, 3797, 4013, 4019, 4211, 4337, 4397, 4673, 4877, 4919, 5233, 5419, 5479, 6011, 6073, 6079, 6131

Offset: 1

Author

Amarnath Murthy, Mar 30 2002

Keywords

• nonn
• base

Comments

Minimum number of digits is taken to be 4 as all 3-digit primes would be trivial members.

Zero may occur only as second digit from left. - Zak Seidov, Dec 28 2020

All the digits after the two first digits from left are necessarily odd. - Bernard Schott, Mar 20 2022

Examples

			11317 is a term as the three substrings of length 3 i.e. 113,131 and 317 all are primes.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A069488 and A069490.

Cf. A211685, A010051, A000040.

Programs

Haskell

a069489 n = a069489_list !! (n-1)
a069489_list = filter g $ dropWhile (<= 1000) a000040_list where
   g x = x < 100 || a010051 (x `mod` 1000) == 1 && g (x `div` 10)
-- Reinhard Zumkeller, Apr 07 2014

Mathematica

Do[ If[ Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 3, 1]]]] == {True}, Print[ Prime[n]]], {n, PrimePi[1000] + 1, 10^3}]
Select[Prime[Range[169,800]],AllTrue[FromDigits/@Partition[ IntegerDigits[ #],3,1], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 05 2019 *)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Apr 12 2002