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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A069488 and A069490.

Cf. A211685, A010051, A000040.

Sequence in context: A166975 A266369 A165295 * A157008 A161404 A252634

Adjacent sequences: A069486 A069487 A069488 * A069490 A069491 A069492

Keyword

nonn,base

Author

Amarnath Murthy, Mar 30 2002

Extensions

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

Status

approved