It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 169 260 131 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 169 260 131, the only two divisors are 1 and 169 260 131. Therefore 169 260 131 is a prime number.
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Since 169260131 is a prime number, 169260131 is also a deficient number, that is to say 169260131 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 169260131 without 169260131 itself (that is 1, by definition!).