OFFSET
1,1
COMMENTS
Minimum number of digits is taken to be 3 as all two-digit primes would be trivial members.
From Robert G. Wilson v, May 12 2014: (Start)
The number of terms below 10^n: 0, 0, 21, 46, 123, 329, 810, 1733, 3985, 9710, ..., .
The least term with n digits is: 113, 1117, 11113, 111119, ..., see A090534.
The largest term with n digits is: 971, 9719, 97973, 979717, ..., see A242377.
The digits 2, 4, 5, 6 and 8 can only appear at the beginning of the prime and the digit 0 never appears. But the digits 1, 3, 7 and 9 can appear anywhere, yet only 1,1 can appear as a pair.
\10^n
d\ 1&2 3 4 5 6 7 8 9 10 Total % @ 10^10
\
1 0 19 34 146 648 1162 2678 8037 22740 39.188034
2 0 0 3 6 27 18 66 175 449 0.816186
3 0 14 19 63 326 712 1526 3855 11040 19.403018
4 0 3 2 13 54 92 143 384 1031 1.895550
5 0 0 0 9 17 24 45 176 426 0.763995
6 0 4 6 4 24 66 146 233 630 1.224834
7 0 14 20 100 436 907 1980 5442 15421 26.875285
8 0 0 3 6 24 25 37 176 388 0.721797
9 0 9 13 38 157 361 763 1790 5125 9.111301
Total 0 63 100 385 1713 3367 7384 20268 57250 100.00000
(End)
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10101 (first 1000 terms from Reinhard Zumkeller)
EXAMPLE
3719 is a term as the three substrings of length 2, i.e., 37, 71 and 19, are all prime.
MATHEMATICA
Do[ If[ Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 2, 1]]]] == {True}, Print[ Prime[n]]], {n, PrimePi[100] + 1, 500}]
PROG
(Haskell)
a069488 n = a069488_list !! (n-1)
a069488_list = filter f $ dropWhile (<= 100) a038618_list where
f x = x < 10 || a010051 (x `mod` 100) == 1 && f (x `div` 10)
-- Reinhard Zumkeller, Apr 07 2014
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Mar 30 2002
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Apr 12 2002
STATUS
approved