## Sets of Primes

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

### Sets of Primes

We have this set of primes which is infinite. This has lots of different subsets. Here is the list of subsets:
Real Eisenstein primes: 3x + 2
Pythagorean primes: 4x + 1
Real Gaussian primes: 4x + 3
Landau primes: x^2 + 1
Central polygonal primes: x^2 - x + 1
Centered triangular primes: 1/2(3x^2 + 3x + 2)
Centered square primes: 1/2(4x^2 + 4x + 2)
Centered pentagonal primes: 1/2(5x^2 + 5x + 2)
Centered hexagonal primes: 1/2(6x^2 + 6x + 2)
Centered heptagonal primes: 1/2(7x^2 + 7x + 2)
Centered decagonal primes: 1/2(10x^2 + 10x + 2)
Cuban primes: 3x^2 + 6x + 4
Star Primes: 6x^2 - 6x + 1
Cubic primes: x^3 + 2
Wagstaff primes: 1/3(2^n + 1)
Mersennes: 2^x - 1
thabit primes: 3 * 2^x - 1
Cullen primes: x * 2^x + 1
Woodall primes: x * 2^x - 1
Double Mersennes: 1/2 * 2^2^x - 1
Fermat primes: 2^2^x + 1
Alternating Factorial Primes: if x! has x being odd than every odd number when you take the factorial positive and every even number negative. Opposite for even indexed factorials. For example 3rd alternating factorial = 1! - 2! + 3!
Primorial primes: First n primes multiplied together - 1
Euclid primes: first n primes multiplied together + 1
Factorial primes: x! + 1 or x! - 1
Leyland primes: m^n + n^m where m can be anything not negative but n has to be greater than 1
Pierpont primes: 2^m * 3^n + 1
Proth primes: n * 2^m + 1 where n < 2^m
Quartan primes: m^4 + n^4
Solinas primes: 2^m ± 2^n ± 1 where 0< n< m
Soundararajan primes: 1^1 + 2^2 ... n^n for any n
Three-square primes: l^2 + m^2 + n^2
Two Square Primes: m^2 + n^2
Twin Primes: x, x+2
Cousin primes: x, x+4
Sexy primes: x, x + 6
Prime triplets: x, x+2, x+6 or x, x+4, x+6
Prime Quadruplets: x, x+2, x+6, x+8
Titanic Primes: x > 10^999
Gigantic Primes: x > 10^9999
Megaprimes: x > 10^999999

Now Here is a question. Can you find a number where all except the powers of 10 ones intersect? Are there more intersections besides that? I will try to do this myself.
caters

Posts: 8
Joined: Sat Mar 15, 2014 11:14 pm

### Re: Sets of Primes

You can't have a number that is both "Pythagorean primes: 4x + 1" and also "Real Gaussian primes: 4x + 3" so I think the intersection that you're looking for is the empty set.
FWT

Posts: 100
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Sets of Primes

FWT wrote:You can't have a number that is both "Pythagorean primes: 4x + 1" and also "Real Gaussian primes: 4x + 3" so I think the intersection that you're looking for is the empty set.

You are right about that. Its like the line being shifted so that it intersects in the negatives.

However there are lots of different intersections between sets that actually have 1 or more primes.
caters

Posts: 8
Joined: Sat Mar 15, 2014 11:14 pm