Authors: Marius Coman
In this paper I make the following two conjectures: (I) there exist an infinity of triplets of consecutive primes [p, q, r] such that the number obtained concatenating p with x then with q then with y then with r, where x is the gap between p and q and y the gap between q and r, is prime. In other words, if we use the operator “]c[“ with the meaning “concatenating to”, p]c[x]c[q]c[y]c[r is prime for an infinity of triplets [p, q, r]. Example: for [p, q, r, x, y] = [11, 13, 17, 2, 4] the number 11213417 is prime; (II) for any pair of consecutive primes [p, q], p ≥ 7, there exist an infinity of primes r such that the number n = p]c[x]c[q]c[y]c[r is prime, where x is the gap between p and q and y the gap between q and r. Example: for [p, q] = [13, 17] there exist r = 61 such that n = 134174461 is prime (x = 4 and y = 44).
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[v1] 2016-04-01 10:57:18
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