It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 166 848 911 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 166 848 911, the only two divisors are 1 and 166 848 911. Therefore 166 848 911 is a prime number.
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Since 166848911 is a prime number, 166848911 is also a deficient number, that is to say 166848911 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 166848911 without 166848911 itself (that is 1, by definition!).