2016•Unpublished venueOpen access
Conjectures on (q+2)]c[n]c[q and (q-4)]c[n]c[q where n is equal to 1]c[2]c[...]c[p and p, q are primes
Marius Coman
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Abstract
In this paper I make the following four conjectures: (I) let n be a number obtained concatenating the positive integers from 1 to p, where p prime of the form 6*k – 1; there exist an infinity of primes q of the form 6*h + 1 such that the number r obtained concatenating q with n then with q + 6 is prime; (II) let n be defined as in Conjecture 1; there exist an infinity of primes q of the form 6*h + 1 such that the number r obtained concatenating q + 6 with n then with q is prime; (III) let n be a number obtained concatenating the positive integers from 1 to p, where p prime of the form 6*k + 1; there exist an infinity of primes q of the form 6*h - 1 such that the number r obtained concatenating q with n then with q + 6 is prime; (IV) let n be defined as in Conjecture 3; there exist an infinity of primes q of the form 6*h - 1 such that the number r obtained concatenating q + 6 with n then with q is prime.