It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 11 607 653 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 11 607 653, the only two divisors are 1 and 11 607 653. Therefore 11 607 653 is a prime number.
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Since 11607653 is a prime number, 11607653 is also a deficient number, that is to say 11607653 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 11607653 without 11607653 itself (that is 1, by definition!).