227 (two hundred ndtwenty-seven) is the natural number between 226 and 228. It is also 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 ...

In mathematics

227 is a

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

and the start of a

prime triplet In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form or . With the exceptions of and , this is the closest possible grouping of t ...

(with 229 and 233). It is a

safe 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 + ...

, as dividing it by two and rounding down produces the

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 + ...

113 113 may refer to: *113 (number), a natural number *AD 113, a year * 113 BC, a year *113 (band), a French hip hop group * 113 (MBTA bus), Massachusetts Bay Transportation Authority bus route * 113 (New Jersey bus), Ironbound Garage in Newark and run ...

. It is also a

regular prime In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli num ...

, a

Pillai prime In number theory, a Pillai prime is a prime number ''p'' for which there is an integer ''n'' > 0 such that the factorial of ''n'' is one less than a multiple of the prime, but the prime is not one more than a multiple of ''n''. To put it algebraical ...

, a Stern prime, and a Ramanujan prime. 227 and 229 form the first twin prime pair for which neither is a cluster prime. The 227th

harmonic number In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \dot ...

is the first to exceed six. There are 227 different

connected graph In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgrap ...

s with eight edges, and 227 independent sets in a 3 × 4

grid graph In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space , forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a latti ...

References

Integers {{Num-stub