It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 31 719 437 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 31 719 437, the only two divisors are 1 and 31 719 437. Therefore 31 719 437 is a prime number.
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Since 31719437 is a prime number, 31719437 is also a deficient number, that is to say 31719437 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 31719437 without 31719437 itself (that is 1, by definition!).