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Let P(N) denote the number of primes of the form n^2+1 for 1<=n<=N, then P(N)∼0.68641li(N), (1) where li(N) is the logarithmic integral (Shanks 1960, pp. 321-332). Let Q(N) ...

The Schnirelmann density of a set of nonnegative integers is the greatest lower bound of the fractions A(n)/n where A(n) is the number of terms in the set <=n.

7 7 6 6 3 1; 6 5 4 2 ; 3 3 ; 2 A descending plane partition of order n is a two-dimensional array (possibly empty) of positive integers less than or equal to n such that the ...

A type of diagram invented by Lewis Carroll (the name is an abbreviation of "Lewis") that can be used to determine the number of minimal covers of n numbers with k members.

When the group order h of a finite group is a prime number, there is only one possible group of group order h. Furthermore, the group is cyclic.

A random partition of a number n is one of the P(n) possible partitions of n, where P(n) is the partition function P. A random partition can be given by RandomPartition[n] in ...

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

An addition chain for a number n is a sequence 1=a_0<a_1<...<a_r=n, such that each member after a_0 is the sum of two earlier (not necessarily distinct) ones. The number r is ...

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. ...