It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 21 077 299 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 21 077 299, the only two divisors are 1 and 21 077 299. Therefore 21 077 299 is a prime number.
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Since 21077299 is a prime number, 21077299 is also a deficient number, that is to say 21077299 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 21077299 without 21077299 itself (that is 1, by definition!).