It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 44 528 921 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 44 528 921, the only two divisors are 1 and 44 528 921. Therefore 44 528 921 is a prime number.
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Since 44528921 is a prime number, 44528921 is also a deficient number, that is to say 44528921 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 44528921 without 44528921 itself (that is 1, by definition!).