People were like "The digits add up to 6, it's clearly divisible by 3" and yes, that's true, but counterpoint:
Just look at it. Look at it, and tell me if you've ever seen a primer-looking number.
If you think 51 not being prime is bad, you should look at 511.
That said, when you convert it to binary, 511 is 111 111 111 [(2^9)-1], which is 111 x 001 001 001, and converting back to decimal is 7 x 73. So of course it's not prime, but at first glance it looks like it should be.
So the math behind this should be pretty easy now that I had a think, since basically the question is for base bigger than 5, we just check (base*5)+1 and so it can't be any odd base since those result in even numbers. And since base 6 is 31 base 8 is 41 etc we just have to check for the first prime
Which lucky us 31 is prime so 51 in base 6 is prime, as well as in base 8 12 and 14. So base 10 is actually kinda special in 51 not being prime. Base 20 is the next prime number.
Okay i thought at first you were asking if the number 51 (as in 3x17) was prime in other bases, and i was like “of course?? Primes don’t depend on bases” this makes more sense lol
