Is 725009513 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 725 009 513 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 725 009 513, the only two divisors are 1 and 725 009 513. Therefore 725 009 513 is a prime number.
As a consequence, 725 009 513 is only a multiple of 1 and 725 009 513.
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Since 725009513 is a prime number, 725009513 is also a deficient number, that is to say 725009513 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 725009513 without 725009513 itself (that is 1, by definition!).