Introduction
To solve the question, we need to find the number of four digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7, which are greater than 3400.

Step 1: Counting the numbers starting with 3
We need to count the number of four digit numbers that start with the digit 3. Since the first digit is fixed, we have 6 choices for the second digit, 6 choices for the third digit, and 6 choices for the fourth digit. Therefore, the number of four digit numbers that start with 3 is 6 x 6 x 6 = 216.

Step 2: Counting the numbers starting with 4, 5, 6, and 7
We also need to count the number of four digit numbers that start with 4, 5, 6, or 7. Since the first digit is greater than 3, we have 4 choices for the first digit. For the second, third, and fourth digits we have 7 choices for each digit. Therefore, the number of four digit numbers that start with 4, 5, 6, or 7 is 4 x 7 x 7 x 7 = 1372.

Step 3: Total number of numbers
The total number of four digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7, which are greater than 3400 is the sum of the numbers we found in Step 1 and Step 2. Therefore, the total number of four digit numbers is 216 + 1372 = 1588.

Conclusion
Therefore, there are 1588 four digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7, which are greater than 3400.