A088884 Primes which when concatenated with their reverse and decremented by 2 yield a new prime.

3, 5, 11, 53, 107, 131, 149, 167, 179, 191, 311, 317, 389, 503, 599, 947, 971, 1049, 1061, 1097, 1187, 1223, 1259, 1427, 1439, 1523, 1571, 1583, 1697, 1721, 1787, 1811, 1871, 1913, 1931, 1949, 3089, 3119, 3191, 3209, 3299, 3449, 3617, 3671, 3677, 3761

Offset: 1

Author

Chuck Seggelin, Oct 21 2003

Keywords

• base
• nonn

Comments

It appears that if concat(p,reverse(p))-2 is prime, then concat(p,reverse(p))+2 is not and vice versa. This was tested for the first 60000 primes.

Conjecture: except for 3, all these primes are of the form 6*k - 1. - Davide Rotondo, Apr 29 2025

Examples

			53 is a term because (i) 53 is prime and (ii) when 53 is concatenated with its reverse (35) - 2, the result (5333) is prime.
		

Links

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

Crossrefs

Cf. A067087 (concatenation of n-th prime and its reverse), A088883 (with incremented rather than decremented).

Programs

Mathematica

Select[Prime[Range[600]],PrimeQ[FromDigits[Join[IntegerDigits[#], Reverse[ IntegerDigits[ #]]]]- 2]&] (* Harvey P. Dale, Apr 06 2017 *)