# 2000 (number)

 ← 1999 2000 2001 →
Cardinal two thousand
Ordinal 2000th
(two thousandth)
Factorization 24× 53
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

• 2001sphenic number
• 2003Sophie Germain prime and the smallest prime number in 2000's
• 2005 – A vertically symmetric number
• 2009$7^4 - 7^3 - 7^2$
• 2011Sexy prime number. Also, sum of eleven consecutive primes: 2011=157+163+167+173+179+181+191+193+197+199+211.
• 2015Lucas–Carmichael number
• 2016triangular number
• 2017Mertens function zero. (2011, 2017) is a sexy prime pair.
• 2020 – sum of the totient function for the first 81 integers
• 2024tetrahedral number
• 2025$45^2$, sum of the cubes of the first nine integers, centered octagonal number
• 2027safe prime
• 2029 – member of the Mian–Chowla sequence
• 2030$21^2 + 22^2 + 23^2 + 24^2$=$25^2 + 26^2 + 27^2$
• 2031centered pentagonal number
• 2039 – Sophie Germain prime, safe prime
• 2047super-Poulet number, Woodall number, decagonal number. Also, 2047 = 211 − 1 = 23 × 89 and is the first Mersenne number that is composite for a prime exponent.
• 2048power of two
• 2056magic constant of n×n normal magic square and n-queens problem for n = 16.
• 2060 – sum of the totient function for the first 82 integers
• 2063 – Sophie Germain prime, safe prime
• 2069 – Sophie Germain prime
• 2070pronic number
• 2080 – triangular number
• 2093 – Mertens function zero
• 2095 – Mertens function zero
• 2096 – Mertens function zero
• 2097 – Mertens function zero
• 2099 – Mertens function zero, safe prime, highly cototient number
• 2100 – Mertens function zero
• 2101centered heptagonal number
• 2107 – member of a Ruth–Aaron pair with 2108 (first definition)
• 2108 – member of a Ruth–Aaron pair with 2107 (first definition)
• 2109square pyramidal number
• 2112 – The break-through album of the band Rush
• 2113 – Mertens function zero, Proth prime, centered square number
• 2116$46^2$
• 2117 – Mertens function zero
• 2119 – Mertens function zero
• 2120 – Mertens function zero
• 2122 – Mertens function zero
• 2125nonagonal number
• 2127 – sum of the first 34 primes
• 2129 – Sophie Germain prime
• 2135 – Mertens function zero
• 2136 – Mertens function zero
• 2138 – Mertens function zero
• 2141 – Sophie Germain prime
• 2142 – sum of the totient function for the first 83 integers
• 2143 – almost exactly 22π4
• 2145 – triangular number
• 2162 – pronic number
• 2166 – sum of the totient function for the first 84 integers
• 2169Leyland number
• 2171 – Mertens function zero
• 2172 – Mertens function zero
• 2178 – reverses when multiplied by 4
• 2175 – smallest number requiring 143 seventh powers for Waring representation
• 2176pentagonal pyramidal number, centered pentagonal number
• 2179Wedderburn–Etherington number
• 2187$3^7$, vampire number, perfect totient number
• 2188Motzkin number
• 2197$13^3$
• 2199 – perfect totient number
• 2201 – only known non-palindromic number whose cube is palindromic; also no known fourth or higher powers are palindromic for non-palindromic numbers
• 2205 – odd abundant number
• 2207 – safe prime, Lucas prime
• 2208Keith number
• 2209$47^2$, centered octagonal number
• 2211 – triangular number
• 2222repdigit
• 2223Kaprekar number
• 2230 – sum of the totient function for the first 85 integers
• 2232 – decagonal number
• 2245 – centered square number
• 2254 – member of the Mian–Chowla sequence
• 2255octahedral number
• 2256 – pronic number
• 2269cuban prime
• 2272 – sum of the totient function for the first 86 integers
• 2273 – Sophie Germain prime
• 2276 – sum of the first 35 primes, centered heptagonal number
• 2278 – triangular number
• 2287balanced prime
• 2294 – Mertens function zero
• 2295 – Mertens function zero
• 2296 – Mertens function zero
• 2299 – member of a Ruth–Aaron pair with 2300 (first definition)
• 2300 – tetrahedral number, member of a Ruth–Aaron pair with 2299 (first definition)
• 2301 – nonagonal number
• 2304$48^2$
• 2306 – Mertens function zero
• 2309primorial prime, Mertens function zero, highly cototient number
• 2310 – fifth primorial
• 2311 – primorial prime
• 2321 – Mertens function zero
• 2322 – Mertens function zero
• 2326 – centered pentagonal number
• 2328 – sum of the totient function for the first 87 integers, the number of groups of order 128, see [1].
• 2331centered cube number
• 2338 – Mertens function zero
• 2339 – Sophie Germain prime
• 2346 – triangular number
• 2351 – Sophie Germain prime
• 2352 – pronic number
• 2357Smarandache–Wellin prime
• 2368 – sum of the totient function for the first 88 integers
• 2378Pell number
• 2379 – member of the Mian–Chowla sequence
• 2381 – centered square number
• 2393 – Sophie Germain prime
• 2397 – sum of the squares of the first ten primes
• 2399 – Sophie Germain prime
• 2400 – perfect score on SAT tests administered after 2005
• 2401$7^4$, $49^2$, centered octagonal number
• 2415 – triangular number
• 2417 – balanced prime
• 2425 – decagonal number
• 2427 – sum of the first 36 primes
• 2431 – product of three consecutive primes
• 2437 – cuban prime
• 2447 – safe prime
• 2450 – pronic number
• 2456 – sum of the totient function for the first 89 integers
• 2458 – centered heptagonal number
• 2459 – Sophie 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
• 2480 – sum of the totient function for the first 90 integers
• 2481 – centered pentagonal number
• 2484 – nonagonal number
• 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$50^2$
• 2501 – Mertens function zero
• 2502 – Mertens function zero
• 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 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 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 OEIS)
• 2521 – 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
• 2543 – Sophie Germain prime
• 2549 – Sophie Germain prime
• 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
• 2579 – safe prime
• 2580 – Keith number
• 2584Fibonacci number, sum of the first 37 primes
• 2596 – sum of the totient function for the first 92 integers
• 2600 – tetrahedral number, member of a Ruth–Aaron pair with 2601 (first definition)
• 2601$51^2$, member of a Ruth–Aaron pair with 2600 (first definition)
• 2620amicable number with 2924
• 2626 – decagonal number
• 2628 – triangular number
• 2632 – number of consecutive baseball games played by Cal Ripken, Jr.
• 2641 – centered pentagonal number
• 2647 – centered heptagonal number
• 2652 – pronic number
• 2656 – sum of the totient function for the first 93 integers
• 2665 – centered square number
• 2674 – nonagonal number
• 2677 – balanced prime
• 2680 – number of 11-queens problem solutions
• 2689 – Mertens function zero, Proth prime
• 2693 – Sophie Germain prime
• 2699 – Sophie Germain prime
• 2701 – triangular number, super-Poulet number
• 2702 – sum of the totient function for the first 94 integers
• 2704$52^2$
• 2719 – largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers.[1] In 1997 it was conjectured that this is also the largest such odd number.[2] It is now known this is true if the generalized Riemann hypothesis is true.[3]
• 2728 – Kaprekar number
• 2729 – highly cototient number
• 2731Wagstaff prime
• 2736 – octahedral number
• 2741 – Sophie Germain prime
• 2744$14^3$
• 2747 – sum of the first 38 primes
• 2753 – Sophie 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
• 2801 - first base 7 repunit prime
• 2806 – centered pentagonal number, sum of the totient function for the first 96 integers
• 2809$53^2$, centered octagonal number
• 2813 – centered square number
• 2819 – Sophie Germain prime, safe prime
• 2821 – Carmichael number
• 2835 – odd abundant number, decagonal number
• 2843 – centered heptagonal prime
• 2850 – triangular number
• 2862 – pronic number
• 2870 – square pyramidal number
• 2871 – nonagonal number
• 2872tetranacci number
• 2879 – safe prime
• 2897Markov number
• 2902 – sum of the totient function for the first 97 integers
• 2903 – Sophie Germain prime, safe prime, balanced prime
• 2914 – sum of the first 39 primes
• 2915 – Lucas–Carmichael number
• 2916$54^2$
• 2924 – amicable number with 2620
• 2925magic constant of n×n normal magic square and n-queens problem for n = 18, tetrahedral number, member of the Mian-Chowla sequence
• 2926 – triangular number
• 2939 – Sophie Germain prime
• 2944 – sum of the totient function for the first 98 integers
• 2963 – Sophie Germain prime, safe prime, balanced prime
• 2965 – greater of second pair of Smith brothers, centered square number
• 2969 – Sophie Germain prime
• 2970harmonic divisor number, pronic number
• 2976 – centered pentagonal number
• 2997 – chiliagonal number
• 2999 – safe prime

## References

1. ^ "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.
2. ^ Ono, Ken (1997). "Ramanujan, taxicabs, birthdates, zipcodes and twists". American Mathematical Monthly 104 (10): 912–917. doi:10.2307/2974471. Retrieved 11 November 2012.
3. ^ Ono, Ken; K Soundararajan (1997). "Ramanujan's ternary quadratic forms". Inventiones Mathematicae 130 (3): 415–454. doi:10.1007/s002220050191. Retrieved 12 November 2012.