After looking at Twin, Cousin, and Sexy primes I notice that the difference between them is always even except for 2. It does make sense since the difference between two odd numbers is an even number and all primes are odd except for 2.

After looking a bit into sexy primes I found that there are also subcategories of sexy primes, as they say sexy constellations. For example there are also sexy triplets, i.e. 7, 13, 19; 31, 37, 43. There are also sexy quadruplets. I also read that they're not called sexy primes because their fabulous. They're called sexy primes because in latin six is sex, thus resulting in sexy primes. hehe : )

After reading more into twin, cousin, and sexy primes, I noticed the names just comes from the difference of the prime numbers. Like twin primes differ by 2, cousin primes differ by 4, and sexy primes differ by 6.

Looking at the prime table, I notice there are a lot of primes that differ by 10: (3, 13), (7, 17), (19, 29), (13, 23), (31, 41) just to name a few. It makes me wonder if there is a name for this kind of prime set, say Decade Primes or something like that. If not, I claim the name!

So apparently there are over 70 different types of classifications for primes. I looked through them, and it seems that there are no definitions for primes that differ by 10 (so the name is yours!). Some of the more eye-catching types included these:

-Centered Decagonal Primes: of the form $5(n^2 - n) + 1$ (this is the closest classification that came to differences by 10, as the differences between the first 7 numbers were 20, 30, 40, 50, 60, and 70 respectively)

-Dihedral Primes: they stay prime when you read them upside down

-Lucky Primes: all the primes that are also lucky numbers…. lucky to whom, I wonder?

-Palindromic Primes: stay the same when read backwards

-Primes in Residue Classes: they are equivalent to d modulo a (connection to Chapter 2!)

-Prime Triplets: primes where either $(p, p+2, p+4)$ or $(p, p+4, p+6)$ are all prime

Some of the classifications had infinite numbers of primes, while one had only a single prime that belonged to it. I find it very interesting that given this set of unique integers, mathematicians can find so many ways to break it down and analyze it.

I wonder who came up with the notion of dihedral primes?? What possible purposes could they serve?

According to Wikipedia:

"In 2006 Phil Carmody found the prime 10127576 + 1081101080188810801011801 × 1063776 + 1.[2] It may be the largest known dihedral prime."