A083966 Numbers n such that the concatenation 2n3n5n7 is prime.

1, 6, 8, 9, 16, 17, 18, 21, 23, 24, 29, 32, 39, 64, 70, 78, 84, 85, 98, 1000, 1005, 1013, 1033, 1038, 1041, 1047, 1056, 1065, 1066, 1076, 1087, 1091, 1102, 1107, 1109, 1115, 1118, 1121, 1137, 1139, 1152, 1156, 1164, 1167, 1171, 1173, 1185, 1199, 1220, 1241

Offset: 1

Author

Farideh Firoozbakht, Jun 15 2003, Jun 19 2003

Keywords

• base
• easy
• nonn

Comments

Numbers n such that the concatenation of 2, n, 3, n, 5, n and 7 is prime.

This concatenation is fp(4, n) as defined in A083677.

For any 3-digit number n, fp(4, n) is divisible by 7, so there are no 3-digit numbers in the sequence.

More generally, there are no (3+6*k)-digit numbers in the sequence for any k. - Robert Israel, Nov 12 2019

Examples

			8 and 21 are in the sequence because 2838587 and 2213215217 are primes.
16 is in the sequence because 2163165167 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032711, A083677, A083969, A092117.

Programs

Maple

filter:= proc(n) local m;
  m:= ilog10(n)+1;
isprime(n*(10 + 10^(m+2)+ 10^(2*m+3))+7+5*10^(m+1)+3*10^(2*m+2)+2*10^(3*m+3))
end proc:
select(filter, [$1..2000]); # Robert Israel, Nov 12 2019

Mathematica

v={};Do[If[PrimeQ[FromDigits[Join[{2},IntegerDigits[n],{3}, IntegerDigits[n],{5},IntegerDigits[n],{7}]]],v=Append[v,n]], {n,1300}];v
Select[Range[1300],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Riffle[ {2,3,5,7}, Table[#,{3}]]]]]&](* Harvey P. Dale, Nov 24 2015 *)

PARI

is(n)=isprime(eval(Str(2,n,3,n,5,n,7))) \\ Charles R Greathouse IV, May 15 2013

Extensions

Edited and extended by David Wasserman, Dec 06 2004

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007