BINARY GOLDBACH-EULER PROBLEM IN THE SET Θ = {6K ±1/K∈N}
The article deals with the properties of even numbers ? > 8 comparable to m by modulo 6, where m = 0, 2, 4 are given by ways to present of even numbers ? = 6? + m as sum of two elements of the set ?. We give a variant of proof binary problem Goldbach –Euler for even numbers ? > 8 presented respectively with the rests m and methods for their representation of elements in the set ?. The binary Goldbach problem and the Euler feasible not only in the set primes P, but and on the set of numbers of twins if the parameters of elements (?1, ?2)?? belong to the set of parameters of number twins Ch = N/FN, где FN where FN – union of parameters of composite numbers in the set ?. We give some examples of decomposition of even numbers ? > 8 using programs Gold –P and Gold Tw. The proof of the infinity of prime numbers in a numerical sequence {6k – 1} & {6k + 1}. On the all presented algorithms are given in the article the description and listings of programs in Software Module ACCESS. That once again shows us that any even number ? > 2 is decomposed into a sum of two prime number.