[viraghr]

Suppose 2 and 7 are the only primes < 15. Then 15 is prime because its prime factorization couldn't contain any other number (2 * 7+1 makes it relatively prime to both 2 and 7 which under the supposition are the only primes < 15.) This is true if we suppose 2 and 7 are the only primes < 15, and that's just what the word "suppose" asks you to entertain.

This little mental exercise proves that 2 and 7 can't be the only primes in existence. It doesn't really matter what 15 really is or isn't. No need to add noise about it. We only care about the supposition, which you cut out of your quote.

Hope this explains why I didn't deal with the true status of new_number! It just doesn't matter.

However, I'm disappointed in you, in the other respondent, and in the moderation here, and I'm glad I made this alternate account.