C++ :: The Value Of 8 Bytes For Unsigned Integers

I'm confused about the actual value of 8 bytes for unsigned integers.

The below code suggests the value is 13217906525252912201:

#include <stdio.h>
#include <inttypes.h>
typedef uint64_t byte_int_t;
int main(void){
byte_int_t t;
printf("%" PRIu64 "
", t);
}

./runprogram
13217906525252912201

However, when I use a calculator, I get a different value: 2^64= 1.8446744e+19

So I was wondering is this really 8 bytes? So I try below test and it produces 8, as expected:

#include <stdio.h>
#include <inttypes.h>
typedef uint64_t byte_int_t;
int main(void) {
byte_int_t t;
printf("%u
", sizeof(t));
return 0;
}

So why does C and my calculator provide two different results?