Number Theory

    

Three Conjectures About an Infinity of Subsets of Integers, Each with Possible Infinite Terms Primes or Squares of Primes

Authors: Marius Coman

In my previous paper «Twenty-four conjectures about “the eight essential subsets of primes”» are made three conjectures about each one from the following eight subsets: the primes of the form 30*k + 1, 30*k + 7, 30*k + 11, 30*k + 13, 30*k + 17, 30*k + 19, 30*k + 23 respectively 30*k + 29. The conjectures from that paper state that each from these eight sets of primes has an infinity of terms and also that each one of them can be entirely defined with a recurrent formula starting from just three given terms. In this paper are generalized the three conjectures for an infinity of subsets, each having possibly an infinity of terms which are primes or squares of primes, subsets of integers of the form 2*p(1)*p(2)*...*p(m)*k + d, where p(1), p(2), ..., p(m) are the first m odd primes, k is a non-null positive integer and d an odd positive integer satisfying certain conditions.

Comments: 3 Pages.

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[v1] 2014-01-28 07:59:49

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