caters
New Member
USA
2 Posts 
Posted  03/19/2014 : 15:46:00

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 Threesquare 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. Once I know the intersections up to 12 digits can I use that to see which sets have more intersections if you go to infinity? I will try to do this myself. Just so you know I am going up to 12 digit primes because that is the largest prime my computer will test without the program taking too long to test it and to be sure I find intersections of the sets.
Here is my work so far: Real Eisentien primes: 5,11,17,23,29,41,47,53,59,71,83,89,101,107,113,131,137,149,167,173,179,191

Edited by  caters on 03/19/2014 17:01:04 

