# 1217

This number is a prime.

The smallest 4-digit prime *p* such that the sum of the
predecessor and successor primes is divisible by 29. [Russo]

The smallest 4-digit prime such that, if its digits are ABCD, AB+CD, and A+B+C+D, they are also each prime. [Opao]

The smallest emirp whose additive and multiplicative persistences both equal its prime digital root. [Beedassy]

Smallest prime p such that (13^p+9^p)/(13+9) is also prime. [Luen]

The first prime p greater than 3 such that 10*p-3 is a perfect cube. [Ewing]

The smallest emirp to have invertible prime prime index. [Bajpai]

The smallest emirp having an emirp prime index *p*
with reversal *q* such that *q*-th prime is also
an emirp. [Beedassy]

Only non-titanic emirp, that is the product of a repunit number and all its truncations minus four, i.e., 111*11*1-4. [Gupta]

The first prime of the form (A^B)*B+(C^D)*D, where A,B,C,D are consecutive Fibonacci numbers (in this case 1,2,3,5). Are there others? [Leonardis]