# 2000 (number)

(Redirected from 2851 (number))
 ← 1999 2000 2001 →
Cardinal two thousand
Ordinal 2000th
(two thousandth)
Factorization 24× 53
Greek numeral ,Β´
Roman numeral MM
Unicode symbol(s) MM, mm
Binary 111110100002
Ternary 22020023
Quaternary 1331004
Quinary 310005
Senary 131326
Octal 37208
Duodecimal 11A812
Vigesimal 50020
Base 36 1JK36

2000 (two thousand) is a natural number following 1999 and preceding 2001.

Two thousand is the highest number expressible using only two unmodified characters in Roman numerals (MM).

Two thousand is also:

## Selected numbers in the range 2001–2999

### 2400 to 2499

• 2400 – perfect score on SAT tests administered after 2005
• 2401 – 74, 492, centered octagonal number[4]
• 2415 – triangular number
• 2417super-prime, balanced prime[31]
• 2425 – decagonal number[10]
• 2427 – sum of the first 36 primes
• 2431 – product of three consecutive primes
• 2437 – cuban prime[30]
• 2447safe prime[5]
• 2450 – pronic number[11]
• 2456 – sum of the totient function for the first 89 integers
• 2458 – centered heptagonal number[13]
• 2459Sophie Germain prime, safe prime[5]
• 2465magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number[37]
• 2470 – square pyramidal number[14]
• 2477super-prime, cousin prime
• 2480 – sum of the totient function for the first 90 integers
• 2481 – centered pentagonal number[7]
• 2484 – nonagonal number[17]
• 2485 – triangular number
• 2491 – member of Ruth–Aaron pair with 2492 under second definition
• 2492 – member of Ruth–Aaron pair with 2491 under second definition

### 2500 to 2599

• 2500 – 502, palindromic in base 7 (102017)
• 2501 – Mertens function zero
• 2502 – Mertens function zero
• 2510 – member of the Mian–Chowla sequence[6]
• 2513 – member of the Padovan sequence[38]
• 2517 – Mertens function zero
• 2519 – the smallest number congruent to 1 (mod 2), 2 (mod 3), 3 (mod 4), ..., 9 (mod 10)
• 2520superior highly composite number; smallest number divisible by numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 12 ; colossally abundant number; Harshad number in several bases. It is also the highest number with more divisors than any number less than double itself.(sequence A072938 in the OEIS) Not only is it the 7th (and last) number with more divisors than any number double itself but it also the 7th number that is highly composite and the lowest common multiple of a consecutive set of integers from 1 (sequence A095921 in the OEIS) which is a property the previous number with this pattern of divisors does not have (360). That is, although 360 and 2520 both have more divisors than any number twice themselves, 2520 is the lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which 60 is) and is not divisible by 1 to 7 (which 420 is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number.(sequence A106037 in the OEIS)
• 2521star number, centered square number[16]
• 2522 – Mertens function zero
• 2523 – Mertens function zero
• 2524 – Mertens function zero
• 2525 – Mertens function zero
• 2530 – Mertens function zero, Leyland number[18]
• 2533 – Mertens function zero
• 2537 – Mertens function zero
• 2538 – Mertens function zero
• 2543Sophie Germain prime
• 2549Sophie Germain prime, super-prime
• 2550 – pronic number[11]
• 2552 – sum of the totient function for the first 91 integers
• 2556 – triangular number
• 2567 – Mertens function zero
• 2568 – Mertens function zero. Also number of digits in the decimal expansion of 1000!, or the product of all natural numbers from 1 to 1000.
• 2570 – Mertens function zero
• 2579safe prime[5]
• 2580Keith number[27]
• 2584Fibonacci number,[39] sum of the first 37 primes
• 2596 – sum of the totient function for the first 92 integers

### 2700 to 2799

• 2701 – triangular number, super-Poulet number[8]
• 2702 – sum of the totient function for the first 94 integers
• 2704 – 522
• 2719super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers.[40] In 1997 it was conjectured that this is also the largest such odd number.[41] It is now known this is true if the generalized Riemann hypothesis is true.[42]
• 2728Kaprekar number[28]
• 2729 – highly cototient number[12]
• 2731Wagstaff prime[43]
• 2736 – octahedral number[29]
• 2741Sophie Germain prime, 400th prime number
• 2744 – 143, palindromic in base 13 (133113)
• 2747 – sum of the first 38 primes
• 2749super-prime, cousin prime with 2753
• 2753Sophie Germain prime, Proth prime[15]
• 2756 – pronic number
• 2774 – sum of the totient function for the first 95 integers
• 2775 – triangular number
• 2780 – member of the Mian–Chowla sequence[6]
• 2783 – member of a Ruth–Aaron pair with 2784 (first definition)
• 2784 – member of a Ruth–Aaron pair with 2783 (first definition)
• 2791 – cuban prime[30]

## References

1. ^ a b "Sloane's A006972 : Lucas-Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
2. ^ "Sloane's A194472 : Erdős-Nicolas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
3. ^ a b c d "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
4. ^ a b c d "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
5. "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
6. "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
7. "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
8. ^ a b "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
9. ^ "Sloane's A003261 : Woodall numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
10. "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
11. "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
12. ^ a b c "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
13. ^ a b c d "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
14. ^ a b c "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
15. ^ a b c "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
16. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
17. "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
18. ^ a b "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
19. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
20. ^ "Sloane's A008918 : Numbers n such that 4*n = (n written backwards)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-14.
21. ^ "Sloane's A001190 : Wedderburn-Etherington numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
22. ^ "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
23. ^ a b "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
24. ^ "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
25. ^ a b "Sloane's A005231 : Odd abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
26. ^ "Sloane's A005479 : Prime Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
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28. ^ a b "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
29. ^ a b "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
30. ^ a b c "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
31. "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
32. ^ "Sloane's A002110 : Primorial numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
33. ^ "Archived copy". Archived from the original on 2007-02-04. Retrieved 2008-01-22..
34. ^ "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
35. ^ "Sloane's A069151 : Concatenations of consecutive primes, starting with 2, that are also prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
36. ^ "Sloane's A000129 : Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
37. ^ a b "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
38. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
39. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
40. ^ "Odd numbers that are not of the form x^2+y^2+10*z^2". The Online Encyclopedia of Integer Sequences. The OEIS Foundation, Inc. Retrieved 13 November 2012.
41. ^ Ono, Ken (1997). "Ramanujan, taxicabs, birthdates, zipcodes and twists" (PDF). American Mathematical Monthly. 104 (10): 912–917. doi:10.2307/2974471. Retrieved 11 November 2012.
42. ^ Ono, Ken; K Soundararajan (1997). "Ramanujan's ternary quadratic forms" (PDF). Inventiones Mathematicae. 130 (3): 415–454. doi:10.1007/s002220050191. Retrieved 12 November 2012.
43. ^ "Sloane's A000979 : Wagstaff primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
44. ^ "Sloane's A144974 : Centered heptagonal prime numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
45. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
46. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
47. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
48. ^ "Sloane's A195163 : 1000-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.