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The set of prime numbers, sometimes denoted P (Derbyshire 2004, p. 163), and implemented in the Wolfram Language as Primes. In the Wolfram Language, a quantity can be tested ...

For N=k·2^n+1 with k odd and 2^n>k, if there exists an integer a such that a^((N-1)/2)=-1 (mod N), then N is prime. A prime of this form is known as a Proth prime.

The doublestruck capital letter Q, Q, denotes the field of rationals. It derives from the German word Quotient, which can be translated as "ratio." The symbol Q first ...

A statistical distribution in which the variates occur with probabilities asymptotically matching their "true" underlying statistical distribution is said to be random.

A pair of consecutive primes whose digits are rearrangements of each other, first considered by A. Edwards in Aug. 2001. The first few are (1913, 1931), (18379, 18397), ...

There exist numbers y_1<y_2<...<y_(n-1), a<y_(n-1), y_(n-1)<b, such that lambda_nu=alpha(y_nu)-alpha(y_(nu-1)), (1) where nu=1, 2, ..., n, y_0=a and y_n=b. Furthermore, the ...

Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

A quantity (such as a statistical median, quartile deviation, etc.), which is calculated from observed data.

Let n be an elliptic pseudoprime associated with (E,P), and let n+1=2^sk with k odd and s>=0. Then n is a strong elliptic pseudoprime when either kP=0 (mod n) or 2^rkP=0 (mod ...

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F. For example, the field of ...