It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 31 719 409 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 31 719 409, the only two divisors are 1 and 31 719 409. Therefore 31 719 409 is a prime number.
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Since 31719409 is a prime number, 31719409 is also a deficient number, that is to say 31719409 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 31719409 without 31719409 itself (that is 1, by definition!).