Find the smallest prime number N such that the following is true:
The largest prime factor of N−1 is A;
The largest prime factor of A−1 is B;
The largest prime factor of B−1 is 7.
To find the smallest prime number N that satisfies the given conditions, we can start by finding the prime factors of 7 first.
The prime factorization of 7 is simply 7 itself, because 7 is a prime number.
Now, let's move on to finding B, the largest prime factor of 7 - 1.
Let's subtract 1 from 7: 7 - 1 = 6
The prime factorization of 6 is 2 * 3.
Since 3 is the largest prime factor of 6, we have found B = 3.
Next, let's find A, the largest prime factor of 3 - 1.
Subtract 1 from 3: 3 - 1 = 2.
The prime factorization of 2 is simply 2 itself, because 2 is a prime number.
Therefore, we have found A = 2.
Finally, we need to find N, the smallest prime number where the largest prime factor of N - 1 is A.
Add 1 to A to find N - 1: 2 + 1 = 3.
So, N - 1 = 3.
To find the smallest prime number N, we simply add 1 to the result: 3 + 1 = 4.
Therefore, the smallest prime number N that satisfies the given conditions is 4.