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A three-dimensional surface with constant vector field on its boundary which traps at least one trajectory which enters it.

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

The prime signature of a positive integer n is a sorted list of nonzero exponents a_i in the prime factorization n=p_1^(a_1)p_2^(a_2).... By definition, the prime signature ...

A prime ideal is an ideal I such that if ab in I, then either a in I or b in I. For example, in the integers, the ideal a=<p> (i.e., the multiples of p) is prime whenever p ...

There are two definitions of the supersingular primes: one group-theoretic, and the other number-theoretic. Group-theoretically, let Gamma_0(N) be the modular group Gamma0, ...

A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and ...

The distinct prime factors of a positive integer n>=2 are defined as the omega(n) numbers p_1, ..., p_(omega(n)) in the prime factorization ...

A Wieferich prime is a prime p which is a solution to the congruence equation 2^(p-1)=1 (mod p^2). (1) Note the similarity of this expression to the special case of Fermat's ...

The symbol p^e∥n means, for p a prime, that p^e|n, but p^(e+1)n.