227 (two hundred ndtwenty-seven) is the natural number between

226 Year 226 ( CCXXVI) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Marcellus (or, less frequently, year 979 ''Ab urbe cond ...

and

228 Year 228 ( CCXXVIII) was a leap year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Modestus and Maecius (or, less frequently, year 981 ''Ab urbe co ...

. It is also a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), 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 ...

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 p ...

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 __NOTOC__ Year 229 (Roman numerals, CCXXIX) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Cassius (or, less frequentl ...

and

233 __NOTOC__ Year 233 ( CCXXXIII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Paternus (or, less frequently, year 986 ...

). 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. 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 nu ...

, 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 A Stern prime, named for Moritz Abraham Stern, is a prime number that is not the sum of a smaller prime and twice the square of a non zero integer. That is, if for a prime ''q'' there is no smaller prime ''p'' and nonzero integer ''b'' such that ...

, and a

Ramanujan prime In mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function. Origins and definition In 1919, Ramanujan published a new proof of Bertrand's postulate which, ...

. 227 and 229 form the first twin prime pair for which neither is a

cluster prime In number theory, a cluster prime is a prime number such that every even positive integer ''k'' ≤ p − 3 can be written as the difference between two prime numbers not exceeding . For example, the number 23 is a cluster prime because ...

. 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, \do ...

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