8000 (eight thousand) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 7999 and preceding 8001. 8000 is the

cube A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...

of 20, as well as the sum of four consecutive integers cubed, 11³ + 12³ + 13³ + 14³. The fourteen tallest mountains on Earth, which exceed 8000 meters in height, are sometimes referred to as

eight-thousander The eight-thousanders are the 14 mountains recognized by the International Mountaineering and Climbing Federation (UIAA) as being more than in height above sea level, and sufficiently independent of neighbouring peaks. There is no precise defin ...

Selected numbers in the range 8001–8999

8001 to 8099

* 8001 –

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

* 8002 –

Mertens function In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive r ...

zero * 8011 – Mertens function zero,

super-prime Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. In other words, if prime numbers are matched ...

* 8012 – Mertens function zero * 8017 – Mertens function zero * 8021 – Mertens function zero * 8039 –

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 +&nbs ...

* 8059 –

* 8069 –

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 +&nbs ...

* 8093 – Sophie Germain prime

8100 to 8199

* 8100 = 90² * 8101 –

* 8111 – Sophie Germain prime * 8117 –

balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, the nth prime number p_n is a balanced ...

* 8119 –

octahedral number In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahedral ...

; 8119/5741 ≈ √2 * 8125 –

pentagonal pyramidal number A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of s ...

* 8128 –

perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...

harmonic divisor number In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are : 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 . ...

, 127th

, 64th

hexagonal number A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...

, eighth 292

-gonal number In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate numbers. Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, ...

, fourth 1356-gonal number * 8147 – safe prime * 8189 –

highly cototient number In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation :x - \phi(x) = k than any other integer below k and above 1. Here, \phi is Euler's totient func ...

* 8190 – harmonic divisor number * 8191 –

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ...

* 8192 = 2¹³

8200 to 8299

* 8208 – base 10

narcissistic number In number theory, a narcissistic number 1 F_ : \mathbb \rightarrow \mathbb to be the following: : F_(n) = \sum_^ d_i^k. where k = \lfloor \log_ \rfloor + 1 is the number of digits in the number in base b, and : d_i = \frac is the value of each d ...

as 8⁴ + 2⁴ + 0⁴ + 8⁴ = 8208 * 8219 –

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 or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...

with 8221 * 8221 –

, twin prime with 8219 * 8233 –

centered heptagonal number A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by ...

* 8243 – Sophie Germain prime * 8256 – triangular number * 8257 – sum of the squares of the first fourteen primes * 8269 –

cuban prime A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''. First series This is the first of these equations: :p = \frac,\ x = ...

of the form ''x'' = ''y'' + 1 * 8273 – Sophie Germain prime * 8281 = 91², sum of the cubes of the first thirteen integers,

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

centered octagonal number A centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are th ...

* 8287 –

8300 to 8399

* 8321 –

super-Poulet number In number theory, a super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d divides 2^d - 2. For example, 341 is a super-Poulet number: it has positive divisors (1, 11, 31, 341), and we have: :(211 − 2) / 11 = 2 ...

* 8326 –

decagonal number In mathematics, a decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of ...

* 8345 - smallest pandigital number in base 6 * 8361 –

Leyland number In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, ...

* 8363 – prime number, number of prime numbers having five digits * 8377 –

* 8385 – triangular number * 8389 –

8400 to 8499

* 8423 – safe prime * 8436 –

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...

* 8437 -

star number In mathematics, a star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n' ...

* 8464 = 92²

8500 to 8599

* 8513 – Sophie Germain prime,

* 8515 – triangular number * 8521 –

sexy prime In number theory, sexy primes are prime numbers that differ from each other by . For example, the numbers and are a pair of sexy primes, because both are prime and 11 - 5 = 6. The term "sexy prime" is a pun stemming from the Latin word for six ...

with 8527 * 8527 –

, sexy prime with 8521 * 8543 – safe prime * 8555 –

square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid (geometry), pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part ...

* 8558 – Large Schröder number * 8576 – centered heptagonal number * 8581 – super-prime

8600 to 8699

* 8625 – nonagonal number * 8646 – triangular number * 8649 = 93², centered octagonal number * 8658 - sum of the first four

perfect numbers In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...

( 6, 28, 496, 8128) and the product of the culturally significant

666 666 may refer to: * 666 (number) * 666 BC, a year * AD 666, a year * The number of the beast, a reference in the Book of Revelation in the New Testament Places * 666 Desdemona, a minor planet in the asteroid belt * List of highways numbered 6 ...

and 13 * 8663 – Sophie Germain prime * 8693 – Sophie Germain prime * 8695 – decagonal number * 8699 – safe prime

8700 to 8799

* 8712 – smallest number that is divisible by its reverse: 8712 = 4 × 2178 (excluding palindromes and numbers with trailing zeros) * 8713 – balanced prime * 8719 –

* 8741 – Sophie Germain prime * 8747 – safe prime, balanced prime,

* 8748 –

3-smooth In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 72 and 15750 = 2 ...

number (2²×3⁷) * 8751 –

perfect totient number In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, one applies the totient function to a number ''n'', apply it again to the resulting totient, and so on, until the number 1 is rea ...

* 8760 - the number of hours in a non-leap year; 365 × 24 * 8761 – super-prime * 8778 – triangular number * 8783 – safe prime * 8784 - the number of hours in a leap year; 366 × 24

8800 to 8899

* 8801 –

magic constant The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...

of ''n'' × ''n'' normal

magic square In mathematics, especially History of mathematics, historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diago ...

and ''n''-Queens Problem for ''n'' = 26. * 8807 –

, sum of eleven consecutive primes (761 + 769 + 773 + 787 + 797 + 809 + 811 + 821 + 823 + 827 + 829) * 8819 – safe prime * 8833 = 88² + 33² * 8836 = 94² * 8839 – sum of twenty-three consecutive primes (313 + 317 + 331 + 337 + 347 + 349 + 353 + 359 + 367 + 373 + 379 + 383 + 389 + 397 + 401 + 409 + 419 + 421 + 431 + 433 + 439 + 443 + 449) * 8849 –

* 8855 – member of a Ruth-Aaron pair (first definition) with 8856 * 8856 – member of a Ruth-Aaron pair (first definition) with 8855 * 8888 -

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". Ex ...

* 8893 -

star prime In mathematics, a star number is a centered number, centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' ...

8900 to 8999

* 8911 –

Carmichael number In number theory, a Carmichael number is a composite number which in modular arithmetic satisfies the congruence relation: : b^n\equiv b\pmod for all integers . The relation may also be expressed in the form: : b^\equiv 1\pmod for all integers b ...

, triangular number * 8923 –

* 8926 – centered heptagonal number * 8933 – the 1,111th prime number * 8944 – sum of the cubes of the first seven primes * 8951 – Sophie Germain prime * 8963 – safe prime * 8964 – number referring to the

1989 Tiananmen Square Protests The Tiananmen Square protests, known within China as the June Fourth Incident, were student-led Demonstration (people), demonstrations held in Tiananmen Square in Beijing, China, lasting from 15 April to 4 June 1989. After weeks of unsucces ...

* 8969 – Sophie Germain prime * 8976 – enneagonal number * 8999 – super-prime

Prime numbers

There are 110

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 ...

s between 8000 and 9000: :8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999

References

{{Integers, 10 Integers