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The Gram series is an approximation to the prime counting function given by G(x)=1+sum_(k=1)^infty((lnx)^k)/(kk!zeta(k+1)), (1) where zeta(z) is the Riemann zeta function ...

The smallest nontrivial taxicab number, i.e., the smallest number representable in two ways as a sum of two cubes. It is given by 1729=1^3+12^3=9^3+10^3. The number derives ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

Levy (1963) noted that 13 = 3+(2×5) (1) 19 = 5+(2×7), (2) and from this observation, conjectured that all odd numbers >=7 are the sum of a prime plus twice a prime. This ...

The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined by "1, ...

The Mathon graphs are three strongly regular graphs on 784 vertices with regular parameters as summarized in the following tables. k spectrum regular parameters 0 ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

Let B dollars be borrowed at an interest rate of i per month, where i is the annual rate divided by 12, and assume the mortgage needs to be paid back in n months. Then the ...

The nth cubic number n^3 is a sum of n consecutive odd numbers, for example 1^3 = 1 (1) 2^3 = 3+5 (2) 3^3 = 7+9+11 (3) 4^3 = 13+15+17+19, (4) etc. This identity follows from ...