260 (two hundred ndsixty) 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

259 Year 259 ( CCLIX) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Aemilianus and Bassus (or, less frequently, year 1012 ''Ab urbe co ...

and preceding 261. It is also the magic constant of the ''n''×''n'' normal magic square and ''n''-queens problem for ''n'' = 8, the size of an actual chess board. 260 is also the magic constant of the Franklin magic square devised by

Benjamin Franklin Benjamin Franklin ( April 17, 1790) was an American polymath who was active as a writer, scientist, inventor, statesman, diplomat, printer, publisher, and political philosopher. Encyclopædia Britannica, Wood, 2021 Among the leading inte ...

. The minor diagonal gives 260, and in addition a number of combinations of two half diagonals of four numbers from a corner to the center give 260. There are 260 days in the Mayan sacred calendar Tzolkin. 260 may also refer to the years AD

260 __NOTOC__ Year 260 ( CCLX) was a leap 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 Saecularis and Donatus (or, less frequently, year 1013 ''Ab ...

and 260 BC.

Integers from 261 to 269

261

261 = 3²·29,

lucky number In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remain ...

nonagonal number A nonagonal number (or an enneagonal number) is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the constr ...

, unique period in base 2, number of possible unfolded

tesseract In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of e ...

patterns.

262

262 = 2·131, meandric number, open meandric number,

untouchable number An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...

happy number In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...

palindrome number A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''pali ...

semiprime In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime ...

, current first uninteresting number (by

Alex Bellos Alexander Bellos (born 1969) is a British writer, broadcaster and mathematics communicator.Alex Bellos He is the author of books about Brazil and mathematics, as well as having a column in ''The Guardian'' newspaper. Education and early life ...

's definition).

263

263 is a prime,

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 + ...

, sum of five consecutive primes (43 + 47 + 53 + 59 + 61), balanced prime,

Chen prime A prime number ''p'' is called a Chen prime if ''p'' + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2''p'' + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingru ...

Eisenstein prime In mathematics, an Eisenstein prime is an Eisenstein integer : z = a + b\,\omega, \quad \text \quad \omega = e^, that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units , itself ...

with no imaginary part, strictly non-palindromic number,

Bernoulli Bernoulli can refer to: People *Bernoulli family of 17th and 18th century Swiss mathematicians: ** Daniel Bernoulli (1700–1782), developer of Bernoulli's principle **Jacob Bernoulli (1654–1705), also known as Jacques, after whom Bernoulli numbe ...

irregular 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 ...

, Euler

Gaussian prime In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as \mathbf /ma ...

, full reptend prime,

Solinas prime In mathematics, a Solinas prime, or generalized Mersenne prime, is a prime number that has the form f(2^m), where f(x) is a low- degree polynomial with small integer coefficients. These primes allow fast modular reduction algorithms and are widely u ...

, Ramanujan prime.

264

264 = 2³·3·11 = number of edges in a 11·11 square grid. The sum of all 2-digit numbers from 264, is 264: 24 + 42 + 26 + 62 + 46 + 64 = 264. 132 and 396 share this property. 264 equals the sum of the squares of the digits of its own square in base 15. This property is shared with 1, 159, 284, 306 and 387.

265

265 = 5·53,

Padovan number In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values :P(0)=P(1)=P(2)=1, and the recurrence relation :P(n)=P(n-2)+P(n-3). The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5 ...

, number of

derangements In combinatorics, combinatorial mathematics, a derangement is a permutation of the elements of a set (mathematics), set, such that no element appears in its original position. In other words, a derangement is a permutation that has no Fixed point ...

of 6 elements,

centered square number In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each cen ...

Smith number In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base. In the case of numbers that are not square-f ...

subfactorial In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. In other words, a derangement is a permutation that has no fixed points. The number of derangements of ...

266

266 = 2·7·19 =

\left\

sphenic number In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definit ...

nontotient In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotien ...

noncototient In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where � ...

repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Example ...

in base 11 (222). 266 is also the index of the largest proper subgroups of the

sporadic group In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. The ...

known as the

Janko group In the area of modern algebra known as group theory, the Janko groups are the four sporadic simple groups '' J1'', '' J2'', '' J3'' and '' J4'' introduced by Zvonimir Janko. Unlike the Mathieu groups, Conway groups, or Fischer groups, t ...

''J''₁.

267

267 = 3·89,

, the number of

groups A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...

of order 64.Number of groups of order ''n''
/ref> 267 is the smallest number n such that n plus a googol is prime.

268

268 = 2²·67,

. 268 is the smallest number whose product of digits is 6 times the sum of its digits.

269

269 is a prime,

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 ...

with 271, sum of three consecutive primes (83 + 89 + 97),

with no imaginary part, highly cototient number, strictly non-palindromic number, full reptend prime

References

{{Integers, 2 Integers