It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 42 154 573 is a prime number.
Indeed, the definition of a prime numbers is to have only 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 42 154 573, the only two divisors are 1 and 42 154 573. Therefore 42 154 573 is a prime number.
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Since 42154573 is a prime number, 42154573 is also a deficient number, that is to say 42154573 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 42154573 without 42154573 itself (that is 1, by definition!).