It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 64 064 051 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 64 064 051, the only two divisors are 1 and 64 064 051. Therefore 64 064 051 is a prime number.
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Since 64064051 is a prime number, 64064051 is also a deficient number, that is to say 64064051 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 64064051 without 64064051 itself (that is 1, by definition!).