A069706 Primes with property that swapping first and last digits also gives a prime.

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 101, 107, 113, 131, 149, 151, 157, 167, 179, 181, 191, 199, 311, 313, 337, 347, 353, 359, 373, 383, 389, 701, 709, 727, 733, 739, 743, 751, 757, 761, 769, 787, 797, 907, 919, 929, 937, 941, 953, 967, 971, 983, 991, 1009, 1013

Offset: 1

Author

Amarnath Murthy, Apr 08 2002

Keywords

• nonn
• base

Comments

This is not the same as A007500, "palindromic" primes.

Examples

			1049 and 9041 both are primes hence both are members.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007500, A069707, A069708.

Programs

Maple

swapdigs:= proc(n) local d;
  d:= ilog10(n);
  n + ((n mod 10)-floor(n/10^d))*(10^d-1);
end proc:
select(isprime and isprime @ swapdigs, [2,seq(2*i+1,i=1..10^4)]); # Robert Israel, Nov 11 2015

Mathematica

Do[t = IntegerDigits[ Prime[n]]; u = t; u[[1]] = t[[ -1]]; u[[ -1]] = t[[1]]; t = FromDigits[u]; If[ PrimeQ[t], Print[ Prime[n]]], {n, 1, 300}]

Python

from sympy import prime, isprime
A069706_list = [2,3,5,7]
for i in range(5,10**6):
    p = prime(i)
    s = str(p)
    if isprime(int(s[-1]+s[1:-1]+s[0])):
        A069706_list.append(p) # Chai Wah Wu, Nov 11 2015

Extensions

Edited and extended by Robert G. Wilson v, Apr 12 2002

Edited by N. J. A. Sloane, Jan 20 2009