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 Cycles. Text
(.pdf).
On Digraphs under x^{2} and x^{2} − 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:
H.C. Williams'
book:
"Edouard Lucas and Primality Testing": Errata
(F. Schwartz, T. Reix) (.pdf) .
P. Ribenboim : "The Small Book of Bigger Primes" : Chapter 2 (Lucas
Sequences).