It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 44 368 937 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 44 368 937, the only two divisors are 1 and 44 368 937. Therefore 44 368 937 is a prime number.
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Since 44368937 is a prime number, 44368937 is also a deficient number, that is to say 44368937 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 44368937 without 44368937 itself (that is 1, by definition!).