## Mersenne and Fermat Numbers

• Two theorems for proving the primality of Fermat numbers, based on Lucas Sequences. Proof (.pdf).
• A LLT-like test for proving the primality of Fermat numbers, based on Lucas Sequences. Proof (.pdf). arXiv R1
• A primality test for Fermat numbers faster than Pépin's test ? Conjecture and bits of history. Paper (.pdf)
• Properties of Mersenne and Fermat numbers. Paper (ToBeCompleted .pdf)
• Generalized Pell Numbers. Paper (.pdf)
• Properties of Pell numbers. Paper (ToBeCompleted .pdf)
• Properties of Pell numbers modulo a prime p = 1 + 8k. Paper  (ToBeCompleted .pdf)
• Properties of LLT numbers modulo a prime Fermat or Mersenne number. Paper (.pdf)
• Properties of a Fermat-like sequence (Yannick Saouter). Paper (.pdf)
• A new LLT-like test for proving the primality of Mersenne numbers, based on Lucas Sequences. Proof (.pdf).
(this test can be derived easily from the original LLT ...)
• A candidate LLT-like test for proving the primality of Mersenne numbers, based on LLT CyclesText (.pdf).
• On Digraphs under x2 and x2 − 2 modulo a Mersenne Prime. Paper (.pdf).
• A LLT-like test for Mersenne numbers, based on cycles of the Digraph under \$x^2-2\$ modulo a Mersenne prime. Conjecture (.pdf)
• Three conjectures dealing with proving Mersenne, Wagstaff and Fermat numbers prime by means of Cycles of the DiGraph under x^2-2. Paper (.pdf).
• A proof of first part of Conjecture 1 (Mersenne) of previous paper my my-self. Paper (.pdf) 2H2008
• A proof of first part of Conjectures 2 and 3 (Wagstaff and Fermat) of previous paper by Robert Gerbicz. Paper (.pdf) 2H2008
• A proof of first part of Conjectures 2 (Wagstaff) of previous paper by Anton Vrba. Paper (.pdf) 2H2008
• A Conjecture about the order of 3 modulo a Mersenne prime. Paper (.pdf) March 2009
• A Property dealing with the order of 3 modulo a Mersenne prime, by ZetaX. Paper (.pdf) 2006/May and 2009/March
• Links, books, mailing-lists, programs, ... around Mersenne and Fermat numbers:

Last update: 10th of June, 2007.