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Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...

A Fermat prime is a Fermat number F_n=2^(2^n)+1 that is prime. Fermat primes are therefore near-square primes. Fermat conjectured in 1650 that every Fermat number is prime ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

The sequence of numbers obtained by letting a_1=2, and defining a_n=lpf(1+product_(k=1)^(n-1)a_k) where lpf(n) is the least prime factor. The first few terms are 2, 3, 7, 43, ...

Consider a Lucas sequence with P>0 and Q=+/-1. A Fibonacci pseudoprime is a composite number n such that V_n=P (mod n). There exist no even Fibonacci pseudoprimes with ...

A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing ...

If p is prime, then p|P(p), where P(p) is a member of the Perrin sequence 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, ... (OEIS A001608). A Perrin pseudoprime is a composite number n ...

The nth Monica set M_n is defined as the set of composite numbers x for which n|[S(x)-S_p(x)], where x = a_0+a_1(10^1)+...+a_d(10^d) (1) = p_1p_2...p_m, (2) and S(x) = ...

A number satisfying Fermat's little theorem (or some other primality test) for some nontrivial base. A probable prime which is shown to be composite is called a pseudoprime ...

The nth Suzanne set S_n is defined as the set of composite numbers x for which n|S(x) and n|S_p(x), where x = a_0+a_1(10^1)+...+a_d(10^d) (1) = p_1p_2...p_m, (2) and S(x) = ...