It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 30 459 353 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 30 459 353, the only two divisors are 1 and 30 459 353. Therefore 30 459 353 is a prime number.
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Since 30459353 is a prime number, 30459353 is also a deficient number, that is to say 30459353 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 30459353 without 30459353 itself (that is 1, by definition!).