Reverse and add is as simple as it sounds, take
n and add it to its digits in reverse order. (e.g. 234 + 432 = 666).
If you apply this process repeatedly some numbers will eventually hit a prime number, and some will never reach a prime.
I currently have
11431 is not prime 11431 + 13411 = 24842 which is not prime 24842 + 24842 = 49684 which is not prime 49684 + 48694 = 98378 which is not prime 98378 + 87389 = 185767 which is prime!
This number hits a prime
In contrast any multiple of 3 will never hit a prime, this is because the all multiples of 3 have a digit sum that is a multiple of 3 and vice versa. Thus reverse and add on a multiple of 3 will always result in a new multiple of 3 and thus never a prime.
Take a positive integer
n and determine if repeatedly reversing and adding will ever result in a prime number. Output a truthy or falsy value. Either truthy for reaches a prime and falsy value for does not or the other way around both are acceptable.
Prime numbers will be considered to reach a prime number in zero iterations.
This is code-golf so try to make your code as short as possible.
True for reaches a prime false for never reaches a prime
11 -> True 11431 -> True 13201 -> True 13360 -> True 13450 -> True 1019410 -> True 1019510 -> True 22 -> False 1431 -> False 15621 -> False 14641 -> False
While I was writing this challenge I discovered a cool trick that makes this problem a good deal easier. It is not impossible without this trick and it is not trivial with it either but it does help. I had a lot of fun discovering this so I will leave it in a spoiler below.
Repeated reverse and add will always hit a multiple of 11 in 6 iterations or less. If it does not hit a prime before it hits a multiple of 11 it will never hit a prime.