2016•viXraOpen access
Two conjectures involving the numbers obtained concatenating a prime p with 9 then with p itself
Marius Coman
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Abstract
In this paper I make the following two conjectures: (I) there exist an infinity of primes q obtained concatenating a prime p with 9 then with p itself (example: p = 104593 is prime and q = 1045939104593 is also prime); (II) there exist an infinity of primes q obtained concatenating a prime p of the form 6*k – 1 with 9 then with p itself and subtracting 2 (example: p = 104471 is prime and q = 1044719104471 – 2 = 1044719104469 is also prime).