8000 (number)

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "8000" number – news · newspapers · books · scholar · JSTOR (June 2016) (Learn how and when to remove this message)

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.^[1]

• 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 = 90²
• 8101 – super-prime
• 8111 – Sophie Germain prime
• 8117 – super-prime, balanced prime
• 8119 – octahedral number;^[2] 8119/5741 ≈ √2
• 8125 – pentagonal pyramidal number^[3]
• 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

• 8208 – base 10 narcissistic number as 8⁴ + 2⁴ + 0⁴ + 8⁴ = 8208^[4]
• 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^[5]
• 8273 – Sophie Germain prime
• 8281 = 91², sum of the cubes of the first thirteen integers, nonagonal number, centered octagonal number
• 8287 – super-prime

• 8321 – super-Poulet number^[6]
• 8326 – decagonal number^[7]
• 8345 - smallest pandigital number in base 6^[8]
• 8361 – Leyland number^[9]
• 8363 – prime number, number of prime numbers having five digits^[10]
• 8377 – super-prime
• 8385 – triangular number
• 8389 – super-prime, twin prime

• 8423 – safe prime
• 8436 – tetrahedral number^[11]
• 8464 = 92²

• 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^[12]
• 8558 – Large Schröder number
• 8576 – centered heptagonal number
• 8581 – super-prime

• 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

• 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^[13]
• 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

• 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

• 8911 – Carmichael number,^[14] 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

There are 110 prime numbers between 8000 and 9000:^[15][16]

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