# 2000 (number)

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

 ← 1999 2000 2001 →
Cardinaltwo thousand
Ordinal2000th
(two thousandth)
Factorization24 × 53
Greek numeral,Β´
Roman numeralMM
Unicode symbol(s)MM, mm
Binary111110100002
Ternary22020023
Octal37208
Duodecimal11A812

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

## 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
• 2415 – triangular number
• 2417super-prime, balanced prime
• 2425 – decagonal number
• 2427 – sum of the first 36 primes
• 2431 – product of three consecutive primes
• 2437 – cuban prime, largest right-truncatable prime in base 5
• 2447safe prime
• 2450 – pronic number
• 2456 – sum of the totient function for the first 89 integers
• 2458 – centered heptagonal number
• 2459Sophie Germain prime, safe prime
• 2465magic constant of n × n normal magic square and n-queens problem for n = 17, Carmichael number
• 2470 – square pyramidal number
• 2471 – number of ways to partition {1,2,3,4,5,6} and then partition each cell (block) into subcells.
• 2477super-prime, cousin prime
• 2480 – sum of the totient function for the first 90 integers
• 2481 – centered pentagonal number
• 2484 – nonagonal number
• 2485 – triangular number, number of planar partitions of 13
• 2491 = 47 * 53, consecutive prime numbers, 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
• 2503 – Friedman prime
• 2510 – member of the Mian–Chowla sequence
• 2513 – member of the Padovan sequence
• 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 prime, centered square number
• 2522 – Mertens function zero
• 2523 – Mertens function zero
• 2524 – Mertens function zero
• 2525 – Mertens function zero
• 2530 – Mertens function zero, Leyland number
• 2533 – Mertens function zero
• 2537 – Mertens function zero
• 2538 – Mertens function zero
• 2543Sophie Germain prime, sexy prime with 2549
• 2549Sophie Germain prime, super-prime, sexy prime with 2543
• 2550 – pronic number
• 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
• 2580Keith number, forms a column on a telephone or PIN pad
• 2584Fibonacci number, sum of the first 37 primes
• 25923-smooth number (25×34)
• 2596 – sum of the totient function for the first 92 integers

### 2700 to 2799

• 2701 – triangular number, super-Poulet number
• 2702 – sum of the totient function for the first 94 integers
• 2704 = 522
• 2707 – model number for the concept supersonic airliner Boeing 2707
• 2719super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers. In 1997 it was conjectured that this is also the largest such odd number. It is now known this is true if the generalized Riemann hypothesis is true.
• 2728Kaprekar number
• 2729 – highly cototient number
• 2731 – the only Wagstaff prime with four digits, Jacobsthal prime
• 2736 – octahedral number
• 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
• 2756 – pronic number
• 2774 – sum of the totient function for the first 95 integers
• 2775 – triangular number
• 2780 – member of the Mian–Chowla sequence
• 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

### Prime numbers

There are 127 prime numbers between 2000 and 3000:

2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999