A simple property of the odd prime numbers

Here are the first odd prime numbers....

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, ....

http://primes.utm.edu/lists/small/10000.txt

By definition, an odd number is that it is an integer of the form n = 2k + 1, where k is an integer.

So, 3 = 2*1 + 1, 5 = 2*2 + 1, 7 = 2*3 + 1, 11 = 2*5 + 1, 13 = 2*6 + 1, 17 = 2*8 + 1, etc.

Notice that....
3 = 2^2 - 1^2
5 = 3^2 - 2^2
7 = 4^2 - 3^2
11 = 6^2 - 5^2
13 = 7^2 - 6^2
17 = 9^2 - 8^2
19 = 10^2 - 9^2
23 = 12^2 - 11^2
etc.

This shows that a prime number p > 2, can be expressed as the difference of two squares, of two specific consecutive numbers.

This is true because 2k + 1 = (k + 1)^2 - k^2