![]() Ībout Wagstaff numbers, there are only Cycles so the LLT does not work here. ![]() ![]() Often, small trees are attached to cycles.Ībout Mersenne and Fermat numbers, the DiGraph is made of one unique big Tree and of many Cycles, with length dividing. Such a DiGraph is made of Trees and Cycles. The complete graph is called a DiGraph under modulo a prime number (see Shallit & Vasiga work). All the possible seeds and the intermediate values that are crossed build a Tree (2 branches lead to 1). There are many possible seeds that can be used but only a small number of fixed (independent of q or n) seeds are known. Using the LLT means that we travel from a seed (4 for Mersennes 5 for Fermats) to 0 after steps for a Mersenne and steps for a Fermat. However, there exist tests that can show that a Wagstaff number is a PRP (Probable Prime), or not. ![]() ![]() These Maths deal with Mersenne, Wagstaff and Fermat numbers, and with primality tests for these numbers.Ībout Mersennes, the « Lucas-Lehmer Test for Mersenne numbers » (LLT in short) is the most efficient primality test ever built for any number.Ībout Fermats, the Pépin test is usually used however I’ve produced a primality test for Fermats that makes use of a LLT with 5 as seed, and I’ve recently discovered that Kustaa Inkeri provided in 1960 a proof of such a LLT with 8 as seed.Ībout Wagstaff numbers, no efficient primality test is known yet. ![]()
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