A069687 Primes that yield another prime on placing a 1 on both sides (as leading and trailing digits).

3, 5, 17, 23, 29, 47, 53, 83, 107, 113, 131, 149, 173, 197, 239, 251, 317, 359, 383, 401, 443, 503, 509, 599, 641, 683, 701, 719, 743, 797, 821, 947, 953, 1031, 1049, 1103, 1109, 1187, 1229, 1277, 1283, 1301, 1373, 1583, 1613, 1619, 1637, 1733, 1847, 1889

Offset: 1

Author

Amarnath Murthy, Apr 06 2002

Keywords

• nonn
• base

Examples

			239 belongs to this sequence as 12391 is also a prime.
947 and 19471 are both primes ==> 947 is in the sequence. [From _José María Grau Ribas_, Jan 22 2012]
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A069688, A069689 & A069690.

Programs

Maple

a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if isprime(parse(cat(1, p, 1))) then break fi
      od; p
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 18 2012

Mathematica

Select[ Range[2000], PrimeQ[ # ] && PrimeQ[ FromDigits[ Insert[ IntegerDigits[ # ], 1, {{1}, {-1}}]]] &]
san[i_]:=1+Prime[i]*10+10^(Floor@Log[10,Prime[i]]+2); Prime@Select[Range[1000],PrimeQ@san[#]&]  (* From José María Grau Ribas, Jan 22 2012 *)
Select[Prime[Range[300]],PrimeQ[FromDigits[Join[{1},IntegerDigits[#],{1}]]]&]  (* Harvey P. Dale, May 18 2012 *)

PARI

forprime( p=1,9999, isprime(10^#Str(p*10)+p*10+1) & print1(p",")) \\ M. F. Hasler, May 18 2012

PARI

A069687_vec(Nmax=10^4)=my(p,d=1);vector(Nmax,i,until(isprime((d+p)*10+1), d<(p=nextprime(p+1))&d*=10);p)  \\ M. F. Hasler, May 19 2012

Extensions

Edited and extended by Robert G. Wilson v, May 03 2002

Corrected and edited following suggestions by H. P. Dale and others by M. F. Hasler, May 18 2012