It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 52 501 is a prime number.
Indeed, the definition of a prime numbers is to have exactly two distinct positive divisors, 1 and itself. A number is a divisor of another number when the remainder of Euclid’s division of the second one by the first one is zero. Concerning the number 52 501, the only two divisors are 1 and 52 501. Therefore 52 501 is a prime number.
Find out more:
Since 52501 is a prime number, 52501 is also a deficient number, that is to say 52501 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 52501 without 52501 itself (that is 1, by definition!).