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A215421
Primes that remain prime when a single digit 9 is inserted between any two consecutive digits or as the leading or trailing digit.
27
7, 19, 37, 41, 199, 239, 311, 587, 661, 941, 967, 1009, 1997, 4993, 4999, 5393, 5651, 6911, 9109, 9397, 9679, 9829, 19417, 20233, 22549, 27397, 29389, 31387, 39989, 71419, 71569, 90599, 91951, 95369, 97103, 98909, 99023, 160009, 225919, 267389, 313991, 328849
OFFSET
1,1
LINKS
EXAMPLE
31387 is prime and also 313879, 313897, 313987, 319387, 391387, 931387.
MAPLE
A215421:=proc(q, x)
local a, b, c, d, i, n, ok;
for n from 1 to q do
a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
a:=ithprime(n); ok:=1;
for i from 0 to b do
c:=a+9*10^i*trunc(a/10^i)+10^i*x; if not isprime(c) then ok:=0; break; fi;
od;
if ok=1 then print(ithprime(n)); fi;
od; end:
A215421(1000, 9);
MATHEMATICA
Select[Prime[Range[30000]], AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #], 9, n], {n, IntegerLength[ #]+1}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 22 2016 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Aug 10 2012
STATUS
approved