Twin primes RSA conjecture

July 19, 2017 | Autor: Thomas McClure | Categoria: Mathematics, Number Theory
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Twin primes RSA conjecture By Thomas McClure M.A. Introduction. Let the challenge number r=p*q be: p, a 64 digit number, and q, a 65 digit number, where (q = p+2) ; that is r is an even number ± 1, that is 64 digits, and root (64) is 32 digits. Taking a constant, Brun's constant, 1.9022 … , which is the sum of the twin primes to 32 digits, [on a PC machine, accurate to 12 decimal digits, means that 20 digits are insignificant, being in error]. So taking the primes in pairs, (prime pairs): (1/3 + 1/5) … to twelve digits, will discover the prime pairs, accurate to 32 digits. That is, 1.9022 … - B, where B = (twin primes)_(-1) = (1/3 + 1/5) + (6n±1)_(-1) - [(odd n_2)_(-1) + (odd n_2±2)_(-1)] - [false pairs, like [23, 25]; 35, 37; [47, 49]; 53, 55; 65, 67; [77, 79]; 83, 85; 95, 97; [119, 121]; any pair, alternating, divisible by 5, 7, 11, etc.] [1/81 = 1/9_2 has no prime pair but 81-2 and 81+2 are false pairs] Removing (1/3 + 1/5) from 1.9022… and every other prime pair, in sequence of n, eliminating false pairs, until zero to the twelfth place gives an approximation to the 32 place for prime pairs, which straddle 32 digits. Since (8/15) is about (1/2) the number of 1.4 is the initial start. [if the remainder contains false pairs …] Taking (6n±1)_(-1) as modulo for the initial start, increase n until modulo is zero or if not, if the remainder is [(odd n_2)_(-1) and (odd n_2±2)_(-1)] , fitting the modulo plus its remainder into the initial start. And Finding the n that describes (6n±1)_(-1). This will find the prime pairs that are 32 digit roots of 64 digits. Crucial Factor. As you add infinitely prime pairs, B , Brun's constant, ceases to change in the twelfth decimal place. This is the crucial factor. [K. Devlin, The Millennium Problems, c. 2002, (p. 56)] This allows one to find that twin primes or prime pairs. Now consider a procedure which randomly chooses an n which finds a prime pair, that is true. That is, it is not a false pair, neither of the two, composite or a square of an odd prime. Subtracting that prime pair, and all prior prime pairs, from Brun's constant, will yield a delta B, which is within the twelfth digit.

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