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A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry (1948) showed that ...

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

A polyomino tiling is a tiling of the plane by specified types of polyominoes. Tiling by polyominoes has been investigated since at least the late 1950s, particularly by S. ...

A prime partition of a positive integer n>=2 is a set of primes p_i which sum to n. For example, there are three prime partitions of 7 since 7=7=2+5=2+2+3. The number of ...

Pronic numbers are figurate numbers of the form P_n=2T_n=n(n+1), where T_n is the nth triangular number. The first few are 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, ... (OEIS ...

A Proth number that is prime, i.e., a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. Factors of Fermat numbers are of this form as long as they ...

The R graph is the graph on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["RGraph"].

A public-key cryptography algorithm which uses prime factorization as the trapdoor one-way function. Define n=pq (1) for p and q primes. Also define a private key d and a ...

A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The ...

The rising sun graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["RisingSunGraph"].