It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 70 946 951 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 70 946 951, the only two divisors are 1 and 70 946 951. Therefore 70 946 951 is a prime number.
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Since 70946951 is a prime number, 70946951 is also a deficient number, that is to say 70946951 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 70946951 without 70946951 itself (that is 1, by definition!).