For the purpose of this challenge, a multi-base prime is a prime which, when written in base 10, is prime in one or more bases smaller than 10 and larger than 1 as well. All single-digit primes are trivially multi-base primes. 11 is also a multi-base prime, as 11 in binary is 3, which is prime (it is also prime in base 4 and base 6). The first few terms are: 2,3,5,7,11,13, 17, 23,31,37,41,43,47,53,61...
Write a program or function that, when given an integer as input, returns/outputs a truthy value if the input is a multi-base prime, and a falsy value if it is not.
An integer between 1 and 10^12.
A truthy/falsy valule, depending on whether the input is a multi-base prime.
3 -> truthy 4 -> falsy 13 -> truthy 2003 -> truthy (Also prime in base 4) 1037 -> falsy (2017 in base 5 but not a prime in base 10)
This is code-golf, lowest score in bytes wins!