Blog Post #68 - What's unique about this series

What are the unique attributes about this series

576, 676, 5476, 5776, 15376, 15876

List all possible observations and is there any other series similar to this

Blog Post #67 - Find the 3 digit number

1. Let's call the number as XYZ
2. XYZ + a ^ 2 = Perfect square while XYZ - a^2 is a Prime number
3. XYZ + b ^ 2 = Perfect square while XYZ - b ^2 is again a Prime number
4. Suffix a digit W and XYZW is a perfect square again
5. XYZ itself is unique in some sense 

Blog Post #66 - What's the next series and why?

Looking at the series below, find the missing numbers

64, 81, 125, 144, 216, 289, ?, ?

Anything else unique about the result?

Blog Post # 65 - What is unique about these sequence of numbers?

I just happened to notice this pattern when I saw two cars with registration numbers 2809 and 1521 earlier today. Needless to say both number caught my attention since they were perfect squares and then tried to see if few more numbers exhibit that pattern

Here's the sequence I am looking at

1521, 2025, 2809, 4225, 4900...

It is obvious that they are perfect squares but there is something unique they exhibit apart from that in a sequence

What is the pattern they exhibit and also give me the next 2 or 3 four digit numbers in that sequence?