743 (seven hundred ndforty three) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal ...

following

742 __NOTOC__ Year 742 ( DCCXLII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. The denomination 742 for this year has been used since the early medieval period, when the Anno Domini calendar era ...

and preceding

744 __NOTOC__ Year 744 ( DCCXLIV) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar. The denomination 744 for this year has been used since the early medieval period, when the Anno Domini calendar e ...

. It is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

. 743 is a

Sophie Germain prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + ...

, because 2 × 743 + 1 = 1487 is also prime. 743 is an

emirp An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as e ...

, because 347 (the reversal of its digits) is prime. There are exactly 743 independent sets in a four-dimensional (16 vertex)

hypercube graph In graph theory, the hypercube graph is the graph formed from the vertices and edges of an -dimensional hypercube. For instance, the cube graph is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. has vertices, e ...

, and exactly 743 connected

cubic graph In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs. A bicubic graph is a cubic bi ...

s with 16 vertices and girth four.

References

{{DEFAULTSORT:743 (Number) Integers