C - Why can't you get address of a register variable?

Question

Why does this code fail at p = &x ?

#include <stdio.h>

int main() {
register int x = 4;
int* p;
p = &x;
x++;
printf("%d",*p);
return 0;
}

Answer 1

Because registers are build into the cpu, they don't have an address.
https://en.wikipedia.org/wiki/Processor_register