It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 562 685 887 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 562 685 887, the only two divisors are 1 and 562 685 887. Therefore 562 685 887 is a prime number.
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Since 562685887 is a prime number, 562685887 is also a deficient number, that is to say 562685887 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 562685887 without 562685887 itself (that is 1, by definition!).