# 8000 (number)

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{{Redirect|8,000|other uses|8000 (disambiguation)}}
{{Infobox number
| number = 8000
| roman = {{Overline|V}}MMM, or {{Overline|VIII}}
| unicode = {{Overline|V}}MMM, {{Overline|v}}mmm, 
{{Overline|VIII}}, {{Overline|viii}}
|lang1=[Armenian](/source/Armenian_numerals)|lang1 symbol=Փ}}
'''8000''' ('''eight thousand''') is the [natural number](/source/natural_number) following [7999](/source/7000_(number)) and preceding 8001.

8000 is the [cube](/source/cube_(arithmetic)) of [20](/source/20_(number)), as well as the sum of four consecutive integers cubed, 11<sup>3</sup> + 12<sup>3</sup> + 13<sup>3</sup> + 14<sup>3</sup>.

The fourteen tallest mountains on Earth, which exceed 8000 meters in height, are sometimes referred to as [eight-thousander](/source/eight-thousander)s.<ref>{{cite web | last = Voiland| first = Adam| title = The Eight-Thousanders| work = The Earth Observatory| publisher = NASA| date =16 December 2013| url = http://earthobservatory.nasa.gov/Features/8000MeterPeaks/| access-date = 12 September 2016 }}</ref>

==Selected numbers in the range 8001–8999==
===8001 to 8099===
* '''8001''' – [triangular number](/source/triangular_number)
* '''8002''' – [Mertens function](/source/Mertens_function) zero
* '''8011''' – Mertens function zero, [super-prime](/source/super-prime)
* '''8012''' – Mertens function zero
* '''8017''' – Mertens function zero
* '''8021''' – Mertens function zero
* '''8039''' – [safe prime](/source/safe_prime)
* '''8059''' – [super-prime](/source/super-prime)
* '''8069''' – [Sophie Germain prime](/source/Sophie_Germain_prime)
* '''8093''' – Sophie Germain prime

===8100 to 8199===
* '''8100''' = 90<sup>2</sup>
* '''8101''' – [super-prime](/source/super-prime)
* '''8111''' – Sophie Germain prime
* '''8117''' – [super-prime](/source/super-prime), [balanced prime](/source/balanced_prime)
* '''8119''' – [octahedral number](/source/octahedral_number);<ref>{{Cite web|url=https://oeis.org/A005900|title=Sloane's A005900 : Octahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-14}}</ref> 8119/5741 ≈ [√2](/source/square_root_of_2)
* '''8125''' – [pentagonal pyramidal number](/source/pentagonal_pyramidal_number)<ref>{{Cite web|url=https://oeis.org/A002411|title=Sloane's A002411 : Pentagonal pyramidal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-14}}</ref>
* '''[8128](/source/8128_(number))''' – [perfect number](/source/perfect_number), [harmonic divisor number](/source/harmonic_divisor_number), 127th [triangular number](/source/triangular_number), 64th [hexagonal number](/source/hexagonal_number), eighth 292[-gonal number](/source/-gonal_number), fourth 1356-gonal number
* '''8147''' – safe prime
* '''8189''' – [highly cototient number](/source/highly_cototient_number)
* '''8190''' – harmonic divisor number
* '''8191''' – [Mersenne prime](/source/Mersenne_prime)
* '''[8192](/source/8192_(number))''' = [2<sup>13</sup>](/source/power_of_two)

===8200 to 8299===
* '''8208''' – base 10 [narcissistic number](/source/narcissistic_number) as 8<sup>4</sup> + 2<sup>4</sup> + 0<sup>4</sup> + 8<sup>4</sup> = 8208<ref>{{Cite OEIS|A005188|Armstrong (or Plus Perfect, or narcissistic) numbers}}</ref>
* '''8219''' – [twin prime](/source/twin_prime) with 8221
* '''8221''' – [super-prime](/source/super-prime), twin prime with 8219
* '''8233''' – [super-prime](/source/super-prime), [centered heptagonal number](/source/centered_heptagonal_number)
* '''8243''' – Sophie Germain prime
* '''8256''' – triangular number
* '''8257''' – sum of the squares of the first fourteen primes
* '''8269''' – [cuban prime](/source/cuban_prime) of the form ''x'' = ''y'' + 1<ref>{{Cite OEIS|A002407|Cuban primes}}</ref>
* '''8273''' – Sophie Germain prime
* '''8281''' = 91<sup>2</sup>, sum of the cubes of the first thirteen integers, [nonagonal number](/source/nonagonal_number), [centered octagonal number](/source/centered_octagonal_number)
* '''8287''' – [super-prime](/source/super-prime)

===8300 to 8399===
* '''8321''' – [super-Poulet number](/source/super-Poulet_number)<ref>{{Cite OEIS|A050217|Super-Poulet numbers}}</ref>
* '''8326''' – [decagonal number](/source/decagonal_number)<ref>{{Cite OEIS|A001107|10-gonal (or decagonal) numbers}}</ref>
* '''8345''' - smallest pandigital number in base 6<ref>{{cite OEIS|A049363|2=a(1) = 1; for n > 1, smallest digitally balanced number in base n}}</ref>
* '''8361''' – [Leyland number](/source/Leyland_number)<ref>{{Cite OEIS|A076980|Leyland numbers}}</ref>
* '''8363''' – prime number, number of prime numbers having five digits<ref>{{Cite OEIS|A006879|Number of primes with n digits.}}</ref>
* '''8377''' – [super-prime](/source/super-prime)
* '''8385''' – triangular number
* '''8389''' – [super-prime](/source/super-prime), [twin prime](/source/twin_prime)

===8400 to 8499===
* '''8423''' – safe prime
* '''8436''' – [tetrahedral number](/source/tetrahedral_number)<ref>{{Cite OEIS|A000292|Tetrahedral numbers}}</ref>
* '''8437''' - [star number](/source/star_number)
* '''8464''' = 92<sup>2</sup>

===8500 to 8599===
* '''8513''' – Sophie Germain prime, [super-prime](/source/super-prime)
* '''8515''' – triangular number
* '''8521''' – [sexy prime](/source/sexy_prime) with 8527
* '''8527''' – [super-prime](/source/super-prime), sexy prime with 8521
* '''8543''' – safe prime
* '''8555''' – [square pyramidal number](/source/square_pyramidal_number)<ref>{{Cite OEIS|A000330|Square pyramidal numbers}}</ref>
* '''8558''' – [Large Schröder number](/source/oeis%3AA006318)
* '''8576''' – centered heptagonal number
* '''8581''' – super-prime

===8600 to 8699===
* '''8625''' – nonagonal number
* '''8646''' – triangular number
* '''8649''' = 93<sup>2</sup>, centered octagonal number
* '''8658''' - sum of the first four [perfect numbers](/source/perfect_numbers) ([6](/source/6_(number)), [28](/source/28_(number)), [496](/source/496_(number)), [8128](/source/8128)) and the product of the culturally significant [666](/source/666_(number)) and [13](/source/13_(number))
* '''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](/source/super-prime)
* '''8741''' – Sophie Germain prime
* '''8747''' – safe prime, balanced prime, [super-prime](/source/super-prime)
* '''8748''' – [3-smooth](/source/3-smooth) number (2<sup>2</sup>×3<sup>7</sup>)
* '''8751''' – [perfect totient number](/source/perfect_totient_number)<ref>{{Cite OEIS|A082897|Perfect totient numbers}}</ref>
* '''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](/source/magic_constant) of ''n'' × ''n'' normal [magic square](/source/magic_square) and [''n''-Queens Problem](/source/Eight_queens_puzzle) for ''n'' = 26.
* '''8807''' – [super-prime](/source/super-prime), sum of eleven consecutive primes (761 + 769 + 773 + 787 + 797 + 809 + 811 + 821 + 823 + 827 + 829)
* '''8819''' – safe prime
* '''8833''' = 88<sup>2</sup> + 33<sup>2</sup>
* '''8836''' = 94<sup>2</sup>
* '''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](/source/super-prime)
* '''8855''' – member of a [Ruth-Aaron pair](/source/Ruth-Aaron_pair) (first definition) with 8856
* '''8856''' – member of a Ruth-Aaron pair (first definition) with 8855
* '''8888''' - [repdigit](/source/repdigit)
* '''8893''' - [star prime](/source/star_prime)

===8900 to 8999===
* '''8911''' – [Carmichael number](/source/Carmichael_number),<ref>{{Cite OEIS|A002997|Carmichael numbers}}</ref> triangular number
* '''8923''' – [super-prime](/source/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](/source/1989_Tiananmen_Square_Protests)
* '''8969''' – Sophie Germain prime
* '''8976''' – [enneagonal number](/source/enneagonal_number)
* '''8999''' – super-prime

===Prime numbers===
There are 110 [prime number](/source/prime_number)s between 8000 and 9000:<ref>{{Cite OEIS|A038823|Number of primes between n*1000 and (n+1)*1000}}</ref><ref>{{cite web |last=Stein |first=William A. |author-link=William A. Stein |title=The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture |url=https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/ |website=wstein.org |date=10 February 2017 |access-date=6 February 2021}}</ref>
: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==
{{Reflist}}

{{Integers|10}}

Category:Integers

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Adapted from the Wikipedia article [8000 (number)](https://en.wikipedia.org/wiki/8000_(number)) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/8000_(number)?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.