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The second Mersenne prime M_3=2^3-1, which is itself the exponent of Mersenne prime M_7=2^7-1=127. It gives rise to the perfect number P_7=M_7·2^6=8128. It is a Gaussian ...

To fit a functional form y=Ae^(Bx), (1) take the logarithm of both sides lny=lnA+Bx. (2) The best-fit values are then a = ...

A polyare is a polyform formed from a polyomino by removing of half of each square such that at least half of the original join between squares is retained. The first few ...

The number 10 (ten) is the basis for the decimal system of notation. In this system, each "decimal place" consists of a digit 0-9 arranged such that each digit is multiplied ...

The Archimedean duals are the 13 duals of the 13 Archimedean solids, sometimes called the Catalan solids. They are summarized in the following table and illustrated below ...

The dual polyhedra of the Archimedean solids, given in the following table. They are known as Catalan solids in honor of the Belgian mathematician who first published them in ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

Let alpha(G) denote the independence number of a graph G. Then the Shannon capacity Theta(G), sometimes also denoted c(G), of G is defined as ...

The number 24 is equal to 4! (four factorial). A number puzzle asks to construct 24 in as many ways possible using elementary mathematical operations on three copies of the ...

666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...