It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 28 633 147 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 28 633 147, the only two divisors are 1 and 28 633 147. Therefore 28 633 147 is a prime number.
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Since 28633147 is a prime number, 28633147 is also a deficient number, that is to say 28633147 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 28633147 without 28633147 itself (that is 1, by definition!).