A054217 Primes p with property that p concatenated with its emirp p' (prime reversal) forms a palindromic prime of the form 'primemirp' (rightmost digit of p and leftmost digit of p' are blended together - p and p' palindromic allowed).

2, 3, 5, 7, 13, 31, 37, 79, 113, 179, 181, 199, 353, 727, 787, 907, 937, 967, 983, 1153, 1193, 1201, 1409, 1583, 1597, 1657, 1831, 1879, 3083, 3089, 3319, 3343, 3391, 3541, 3643, 3853, 7057, 7177, 7507, 7681, 7867, 7949, 9103, 9127, 9173, 9209, 9439, 9547, 9601

Offset: 1

Author

Patrick De Geest, Feb 15 2000

Keywords

• nonn
• base
• nice

Comments

Original idea from G. L. Honaker, Jr..

Examples

			E.g., prime 113 has emirp 311 and 11311 is a palindromic prime, so 113 is a term.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054218, A000040, A006567, A048054, A002385.

Programs

Mathematica

empQ[n_]:=Module[{idn=IntegerDigits[n],rev},rev=Reverse[idn];And@@PrimeQ[ {FromDigits[ rev],FromDigits[Join[Most[idn],rev]]}]]; Select[Prime[ Range[ 1200]],empQ] (* Harvey P. Dale, Mar 26 2013 *)

Python

from sympy import isprime
def ok(n):
    if not isprime(n): return False
    s = str(n); srev = s[::-1]
    return isprime(int(srev)) and isprime(int(s[:-1] + srev))
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Nov 17 2023

Extensions

Corrected (a(30)=3089 inserted) by Harvey P. Dale, Mar 26 2013