8000 (eight thousand) 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 7999 and preceding 8001. 8000 is the cube 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-thousanders.

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 i ...

* 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 re ...

zero * 8011 – Mertens function zero, super-prime * 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 + ...

* 8059 – super-prime * 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 + ...

* 8093 – Sophie Germain prime

8100 to 8199

* 8100 = 90² * 8101 – super-prime * 8111 – Sophie Germain prime * 8117 – super-prime, balanced prime * 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 ''n''th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahed ...

; 8119/5741 ≈ √2 * 8125 –

pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...

* 8128 –

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

harmonic divisor number In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are: : 1, 6, 2 ...

, 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 represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers. Definition and examples ...

, fourth 1356-gonal number * 8147 – safe prime * 8189 – highly cototient number * 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 17th ...

* 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 (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...

with 8221 * 8221 – super-prime, twin prime with 8219 * 8233 – super-prime,

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 and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the constr ...

centered octagonal number A centered octagonal number is a 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 the same as the od ...

* 8287 – super-prime

8300 to 8399

* 8321 –

super-Poulet number 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 and we have: :(211 - 2) / 11 = 2046 / 11 = 186 :(231 - 2) ...

* 8326 –

decagonal number 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 decagonal number ...

* 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, 177, ...

* 8377 – super-prime * 8385 – triangular number * 8389 – super-prime,

8400 to 8499

* 8423 – safe prime * 8436 –

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

* 8464 = 92²

8500 to 8599

* 8513 – Sophie Germain prime, super-prime * 8515 – triangular number * 8521 –

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

with 8527 * 8527 – super-prime, sexy prime with 8521 * 8543 – safe prime * 8555 – square pyramidal number * 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 divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. T ...

( 6, 28,

496 __NOTOC__ Year 496 ( CDXCVI) was a leap year starting on Monday (link will display the full calendar) of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Paulus without colleague (or, less frequently, ye ...

, 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 * U.S. Route 666, an America ...

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 – super-prime * 8741 – Sophie Germain prime * 8747 – safe prime, balanced prime, super-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 whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × ...

number (2²×3⁷) * 8751 – perfect totient number * 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 of ''n'' × ''n'' normal magic square and ''n''-Queens Problem for ''n'' = 26. * 8807 – super-prime, 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 – super-prime * 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. Example ...

8900 to 8999

* 8911 –

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

, triangular number * 8923 – super-prime * 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 in Chinese as the June Fourth Incident (), were student-led demonstrations held in Tiananmen Square, Beijing during 1989. In what is known as the Tiananmen Square Massacre, or in Chinese the June Fourth ...

* 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 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 ...

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