It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 23 030 407 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 23 030 407, the only two divisors are 1 and 23 030 407. Therefore 23 030 407 is a prime number.
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Since 23030407 is a prime number, 23030407 is also a deficient number, that is to say 23030407 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 23030407 without 23030407 itself (that is 1, by definition!).