Authors: Marius Coman
In this paper I make the following four conjectures: (I) there exist an infinity of primes p of the form (6*k - 1)]c[(6*k + 1)]c[(6*k - 1), where “]c[“ means “concatenated to" (example: for k = 4, the number p = 232523 is prime); (II) there exist an infinity of primes q of the form (6*k + 1)]c[(6*k - 1)]c[(6*k + 1) (example: for k = 2, the number p = 131113 is prime); (III) there exist an infinity of pairs of primes (p, q) = ((6*k - 1)]c[(6*k + 1)]c[(6*k - 1), ((6*k + 1)]c[(6*k – 1)]c[(6*k + 1)); example: for k = 5, (p, q) = (293129, 32931); note that, for such a pair (p, q), q – p = 19802; 1998002; 199980002 and so on; (IV) there exist, for any h positive integer, an infinity of primes q = p + m, where p is prime and m is the number obtained concatenating 1 with a number of h digits of 9 then with 8 then with the same number of h digits of 0 then with 2.
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[v1] 2016-03-24 07:52:47
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