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Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

Cubic lattice sums include the following: b_2(2s) = sum^'_(i,j=-infty)^infty((-1)^(i+j))/((i^2+j^2)^s) (1) b_3(2s) = ...

Legendre's constant is the number 1.08366 in Legendre's guess at the prime number theorem pi(n)=n/(lnn-A(n)) with lim_(n->infty)A(n) approx 1.08366. Legendre first published ...

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

Mills' theorem states that there exists a real constant A such that |_A^(3^n)_| is prime for all positive integers n (Mills 1947). While for each value of c>=2.106, there are ...

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a ...

Let x:U->R^3 be a regular patch, where U is an open subset of R^2. Then (partiale)/(partialv)-(partialf)/(partialu) = eGamma_(12)^1+f(Gamma_(12)^2-Gamma_(11)^1)-gGamma_(11)^2 ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

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 ...

Let Sigma(n)=sum_(i=1)^np_i (1) be the sum of the first n primes (i.e., the sum analog of the primorial function). The first few terms are 2, 5, 10, 17, 28, 41, 58, 77, ... ...