Can you just tell me what id the meaning of the answer {{x}} when i choose a prime number in the equation:

n=17393
eq1=n/(n-x)==n;
a={x}/.Solve[{eq1},{x},Modulus->n]
a+n

Further to the nice hint provided by Mariusz Iwaniuk:

n = 17393;
eq1 = n/(n - x) == n;
Solve[{eq1}, {x}, Modulus -> n]

Out[568]= {{}}

Upshot: Any element in the prime field Z_17393 is a solution.

I broke the record of prime number digits... discovered a prime number check code that gives {x} as a result when the number is prime...and when the number is not prime gives a list of results. .. when the number is too large...and it is not prime, as the list is too large, it does not work and sends a certain message saying that it is not possible to solve all the results...but when the expected result is {x } it doesn't send any message and doesn't send a result... so I put a number that I had gotten by another method and it ran running without sending any message...it was a 100000000 digit number that, according to my table, had to be prime...the problem is that for me to win the $100,000 prize I would have to have a certificate of a scientifically validated method...and this method doesn't work well for giant numbers that aren't Mersenne type, which are prime numbers of formula (2^n)-1