8000 (number)

{{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|lang1 symbol=Փ}} '''8000''' ('''eight thousand''') is the natural number 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.<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 * '''8002''' – Mertens function zero * '''8011''' – Mertens function zero, super-prime * '''8012''' – Mertens function zero * '''8017''' – Mertens function zero * '''8021''' – Mertens function zero * '''8039''' – safe prime * '''8059''' – super-prime * '''8069''' – Sophie Germain prime * '''8093''' – Sophie Germain prime

===8100 to 8199=== * '''8100''' = 90² * '''8101''' – super-prime * '''8111''' – Sophie Germain prime * '''8117''' – super-prime, balanced prime * '''8119''' – 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 * '''8125''' – 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''' – perfect number, harmonic divisor number, 127th triangular number, 64th hexagonal number, eighth 292-gonal number, fourth 1356-gonal number * '''8147''' – safe prime * '''8189''' – highly cototient number * '''8190''' – harmonic divisor number * '''8191''' – Mersenne prime * '''8192''' = 2¹³

===8200 to 8299=== * '''8208''' – base 10 narcissistic number as 8⁴ + 2⁴ + 0⁴ + 8⁴ = 8208<ref>{{Cite OEIS|A005188|Armstrong (or Plus Perfect, or narcissistic) numbers}}</ref> * '''8219''' – twin prime with 8221 * '''8221''' – super-prime, twin prime with 8219 * '''8233''' – super-prime, centered heptagonal number * '''8243''' – Sophie Germain prime * '''8256''' – triangular number * '''8257''' – sum of the squares of the first fourteen primes * '''8269''' – cuban prime of the form ''x'' = ''y'' + 1<ref>{{Cite OEIS|A002407|Cuban primes}}</ref> * '''8273''' – Sophie Germain prime * '''8281''' = 91², sum of the cubes of the first thirteen integers, nonagonal number, centered octagonal number * '''8287''' – super-prime

===8300 to 8399=== * '''8321''' – super-Poulet number<ref>{{Cite OEIS|A050217|Super-Poulet numbers}}</ref> * '''8326''' – 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<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 * '''8385''' – triangular number * '''8389''' – super-prime, twin prime

===8400 to 8499=== * '''8423''' – safe prime * '''8436''' – tetrahedral number<ref>{{Cite OEIS|A000292|Tetrahedral numbers}}</ref> * '''8437''' - star number * '''8464''' = 92²

===8500 to 8599=== * '''8513''' – Sophie Germain prime, super-prime * '''8515''' – triangular number * '''8521''' – sexy prime with 8527 * '''8527''' – super-prime, sexy prime with 8521 * '''8543''' – safe prime * '''8555''' – square pyramidal number<ref>{{Cite OEIS|A000330|Square pyramidal numbers}}</ref> * '''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 (6, 28, 496, 8128) and the product of the culturally significant 666 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 number (2²×3⁷) * '''8751''' – 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 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 * '''8893''' - star prime

===8900 to 8999=== * '''8911''' – Carmichael number,<ref>{{Cite OEIS|A002997|Carmichael numbers}}</ref> 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 * '''8969''' – Sophie Germain prime * '''8976''' – enneagonal number * '''8999''' – super-prime

===Prime numbers=== There are 110 prime numbers 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