8000 (number)

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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]

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;^[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

8200 to 8299[]

• 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

8300 to 8399[]

• 8321 – super-Poulet number^[6]
• 8326 – decagonal number^[7]
• 8361 – Leyland number^[8]
• 8377 – super-prime
• 8385 – triangular number
• 8389 – super-prime, twin prime

8400 to 8499[]

• 8423 – safe prime
• 8436 – tetrahedral number^[9]
• 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^[10]
• 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^[11]
• 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

8900 to 8999[]

• 8911 – Carmichael number,^[12] triangular number
• 8923 – super-prime
• 8926 – centered heptagonal 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:^[13][14]

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[]