8000 (number)

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.

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; 8119/5741 ≈ √2
• 8125 – pentagonal pyramidal number
• 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
• 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
• 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
• 8326 – decagonal number
• 8345 - smallest pandigital number in base 6
• 8361 – Leyland number
• 8363 – prime number, number of prime numbers having five digits
• 8377 – super-prime
• 8385 – triangular number
• 8389 – super-prime, twin prime

8400 to 8499

• 8423 – safe prime
• 8436 – tetrahedral number
• 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
• 8558 –
• 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 (2²ÃƒÂ—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
• 8893 - star prime

8900 to 8999

• 8911 – Carmichael number, 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:

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