It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 22 363 433 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 22 363 433, the only two divisors are 1 and 22 363 433. Therefore 22 363 433 is a prime number.
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Since 22363433 is a prime number, 22363433 is also a deficient number, that is to say 22363433 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 22363433 without 22363433 itself (that is 1, by definition!).