Logical Flaw In Your Code

You need to have a clear understanding on how overflow/underflow works,

  if (studentsNUMBER < 0 or studentsNUMBER > 32767){
    ...
  }

You have declared studentsNUMBER as an integer whose max value can be 32767. Now you are comparing studentNUMBER > 32767 which is will never be the case as studentNUMBER will never be able to cross the limit.

Suggestions

Mind that once there has been overflow/underflow, Undefined Behavior is occurred and your program can do anything abnormal.

One of many approaches to overcome such situation can be like,

long result, 
int studentNUMBER, keyENTERED;
...
result = (studentsNUMBER * 10) + keyENTERED;
if (result > 32767)
{
    // overflow occurred 
}

Hope you will get a concept.

If you look in the log window you will see the compiler complains about an integer overflow calculating (410*410). It is treating 410 as a 16 bit integer, so overflows at 65534. You need to tell the compiler that you are using the long type.

unsigned long Potencia = long(410)*long(410); or unsigned long Potencia = (410L*410L);

Interesting problem. If you watch log window while compiling and you see red text flying by, it means there is a compiler warning. You can click in the log window, press <Ctrl>A then <Ctrl>C to copy the log. Then you can paste into Notepad with <Ctrl>V so you can review the results.

warning: integer overflow in expression [-Woverflow]
Potencia = (410*410) ;
                 ^

You can specify the type of a number using suffixes such as L, LL, UL and such. If you don't specify the type this way, all integers that are small enough to fit in an int will be of type int. When you write

ADV_INTERVAL_MIN_MS * 1000

it gets expanded by the preprocessor to

50 * 1000

Since both arguments are of type int, the compiler will use this type to compute the result. However, the result is 50,000, and on 16-bit systems the largest number that can fit in an int is 32,767, thus the overflow.

As suggested by Majenko, the simple solution is to add the L suffix (for long) to either operand. The compiler will then do the arithmetics using the long data type.

Change that line to:

esp_sleep_enable_timer_wakeup((uint64_t) TIME_TO_SLEEP * 60 * uS_TO_S_FACTOR);

That forces the compiler to do 64-bit arithmetic on the constant rather than defaulting to "int" arithmetic.