Introduction:
In this question, we are given that every telephone number consists of 7 digits, and we need to determine the total number of telephone numbers that can be formed using only the digits 2, 3, 5, and 7.

Approach:
To solve this problem, we can use the concept of permutations and combinations. Since we have 4 digits (2, 3, 5, and 7) to choose from for each of the 7 positions, we can calculate the total number of telephone numbers using the formula for permutations.

Explanation:
Let's break down the problem step by step:

Step 1: Determine the number of choices for each digit
- Since each digit can be chosen from the set {2, 3, 5, 7}, there are a total of 4 choices for each digit.

Step 2: Determine the total number of possibilities
- Since there are 7 positions, and each position can have 4 choices, the total number of possibilities is given by 4 * 4 * 4 * 4 * 4 * 4 * 4 = 4^7 = 16384.

Step 3: Verify the answer
- To ensure that our answer is correct, we can check by counting the total number of telephone numbers manually.
- Since there are 4 choices for each digit, we can count the number of telephone numbers as follows:
- For the first digit, we have 4 choices (2, 3, 5, or 7).
- Similarly, for the second, third, fourth, fifth, sixth, and seventh digits, we also have 4 choices each.
- Therefore, the total number of telephone numbers is 4 * 4 * 4 * 4 * 4 * 4 * 4 = 16384.

Conclusion:
In conclusion, there are a total of 16384 telephone numbers that can be formed using only the digits 2, 3, 5, and 7. This is calculated using the concept of permutations, where each digit has 4 choices and there are 7 positions to fill.