cp's OEIS Frontend

A base-2 Fermat pseudoprime is a composite number x such that 2^x == 2 (mod x). For such an x, ord(2,x) is the smallest positive integer m such that 2^m == 1 (mod x). For a number x to have order n, it must be a factor of 2^n-1 and not be a factor of 2^r-1 for rA086249 lists the number of pseudoprimes of order n.

A base-2 Fermat pseudoprime is a composite number x such that 2^x = 2 mod x.

A composite divisor d of M(m) := 2^m - 1 is called primitive if M(k) != 0 for any k < m.

A primitive composite divisor d of M(m) is said to have rank m, and we write rank(d)=m.

Let M(m)=2^m-1, and define D to be the set of all numbers d such that d|M(m), d==1 (mod m), and rank(d)=m. Then each element d from D is an odd pseudoprime, because if m|d-1, then M(m)|M(d-1) and thus d|M(d-1). The set D contains all composite and primitive divisors d|M(m) that have rank(d)=m and each odd pseudoprime d with rank(d)=m generates only one class [a(n)] with all pseudoprimes d, where a(n)=m, if a(n) is defined as below. See attached file with examples of pseudoprimes.