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The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

The set of numbers generated by excluding the sums of two or more consecutive earlier members is called the prime numbers of measurement, or sometimes the segmented numbers. ...

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 ...

A prime power is a prime or integer power of a prime. A test for a number n being a prime is implemented in the Wolfram Language as PrimePowerQ[n]. The first few prime powers ...

An Abelian planar difference set of order n exists only for n a prime power. Gordon (1994) has verified it to be true for n<2000000.

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

The product of primes p_n#=product_(k=1)^np_k, (1) with p_n the nth prime, is called the primorial function, by analogy with the factorial function. Its logarithm is closely ...

Let pi_(m,n)(x) denote the number of primes <=x which are congruent to n modulo m (i.e., the modular prime counting function). Then one might expect that ...

A prime constellation of four successive primes with minimal distance (p,p+2,p+6,p+8). The term was coined by Paul Stäckel (1892-1919; Tietze 1965, p. 19). The quadruplet (2, ...

Let a!=b, A, and B denote positive integers satisfying (a,b)=1 (A,B)=1, (i.e., both pairs are relatively prime), and suppose every prime p=B (mod A) with (p,2ab)=1 is ...