When you multiply two prime numbers, the product will have at least two distinct prime factors: the two prime numbers being multiplied.
Technically, it is not true that the prime numbers being multiplied need to be distinct. For example, 2*2=4 is the product of two prime numbers, but it is not the product of two distinct prime numbers.
As a result, it is impossible to determine the sum of the largest and second largest prime numbers, since neither of these can be definitively identified.
This seems wrong: “neither can be definitively identified” makes it sound like they exist but just can’t be identified...
Thanks for reviewing and catching these subtle issues!
Technically, it is not true that the prime numbers being multiplied need to be distinct. For example, 2*2=4 is the product of two prime numbers, but it is not the product of two distinct prime numbers.
Good point, I’ve marked this as an error. My prompt about gcd did specify distinctness but the prompt about product did not, so this is indeed an error.
This seems wrong: “neither can be definitively identified” makes it sound like they exist but just can’t be identified...
I passed on this one as being too minor to mark.
Safe primes area subset of Sophie Germain primes
Not true, e.g. 7 is safe but not Sophie Germain.
Good point; I missed reading this sentence originally. I’ve marked this one as well.
Technically, it is not true that the prime numbers being multiplied need to be distinct. For example, 2*2=4 is the product of two prime numbers, but it is not the product of two distinct prime numbers.
This seems wrong: “neither can be definitively identified” makes it sound like they exist but just can’t be identified...
Not true, e.g. 7 is safe but not Sophie Germain.
Thanks for reviewing and catching these subtle issues!
Good point, I’ve marked this as an error. My prompt about gcd did specify distinctness but the prompt about product did not, so this is indeed an error.
I passed on this one as being too minor to mark.
Good point; I missed reading this sentence originally. I’ve marked this one as well.