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- - **Orders of consecutive elements does not exceed floor(sqrt(p))**
(*https://www.mersenneforum.org/showthread.php?t=25360*)

Orders of consecutive elements does not exceed floor(sqrt(p))For some prime p, let m = ord[SUB]p[/SUB](2) be the multiplicative order of 2 mod p, and m[SUB]2[/SUB] = ord[SUB]p[/SUB](3) be the order of 3 mod p. Let L be the least common multiple of m and m[SUB]2[/SUB] (L = lcm(m,m[SUB]2[/SUB])).
Does a prime p exist such that L < sqrt(p) or simply floor(sqrt(p)) ? (There is no such prime below 10^9) The question in general is, for integers (a,b) (a ≠ b[SUP]i[/SUP] for some i > 2 or vice versa) are there finitely many primes p such that: L > floor(sqrt(p)) where L = lcm(m,m[SUB]2[/SUB]) m = ord[SUB]p[/SUB](a) and m[SUB]2[/SUB] = ord[SUB]p[/SUB](b) ? |

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