It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 36 844 921 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 36 844 921, the only two divisors are 1 and 36 844 921. Therefore 36 844 921 is a prime number.
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Since 36844921 is a prime number, 36844921 is also a deficient number, that is to say 36844921 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 36844921 without 36844921 itself (that is 1, by definition!).