It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 122 036 207 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 122 036 207, the only two divisors are 1 and 122 036 207. Therefore 122 036 207 is a prime number.
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Since 122036207 is a prime number, 122036207 is also a deficient number, that is to say 122036207 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 122036207 without 122036207 itself (that is 1, by definition!).