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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 + 2Pythagorean primes: 4x + 1Real Gaussian primes: 4x + 3Landau primes: x^2 + 1Central polygonal primes: x^2 - x + 1Centered 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 + 4Star Primes: 6x^2 - 6x + 1Cubic primes: x^3 + 2Wagstaff primes: 1/3(2^n + 1)Mersennes: 2^x - 1thabit primes: 3 * 2^x - 1Cullen primes: x * 2^x + 1Woodall primes: x * 2^x - 1Double Mersennes: 1/2 * 2^2^x - 1Fermat primes: 2^2^x + 1Alternating 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 - 1Euclid primes: first n primes multiplied together + 1Factorial primes: x! + 1 or x! - 1Leyland primes: m^n + n^m where m can be anything not negative but n has to be greater than 1Pierpont primes: 2^m * 3^n + 1Proth primes: n * 2^m + 1 where n < 2^mQuartan primes: m^4 + n^4Solinas primes: 2^m ± 2^n ± 1 where 0< n< mSoundararajan primes: 1^1 + 2^2 … n^n for any nThree-square primes: l^2 + m^2 + n^2Two Square Primes: m^2 + n^2Twin Primes: x, x+2Cousin primes: x, x+4Sexy primes: x, x + 6Prime triplets: x, x+2, x+6 or x, x+4, x+6Prime Quadruplets: x, x+2, x+6, x+8Titanic Primes: x > 10^999Gigantic Primes: x > 10^9999Megaprimes: x > 10^999999Now 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
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