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A069489 Primes > 1000 in which every substring of length 3 is also prime. 55
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A166975 A266369 A165295 * A157008 A161404 A252634
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Mar 30 2002
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Apr 12 2002
STATUS
approved

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Last modified April 25 10:34 EDT 2024. Contains 371967 sequences. (Running on oeis4.)