2000 (number)

Updated on Dec 07, 2024

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2000 2001 → Factorization 2× 5 Unicode symbol(s) MM, mm		Cardinal two thousand Roman numeral MM
Ordinal 2000th(two thousandth)

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:

In the name of the products Lever 2000 and Grecian 2000, Windows 2000

In Star Trek, the registry number of the USS Excelsior, NX-2000 in Star Trek III: The Search for Spock, and NCC-2000 commanded by Hikaru Sulu in Star Trek VI: The Undiscovered Country.

The postal code for Antwerp (Belgium), Frederiksberg (Denmark), and Sydney (Australia)

Selected numbers in the range 2001–2999

2001 – sphenic number

2003 – Sophie Germain prime and the smallest prime number in the 2000s

2005 – A vertically symmetric number

2009 – 7⁴ − 7³ − 7²

2011 – Sexy prime number. Also, sum of eleven consecutive primes: 2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211.

2015 – Lucas–Carmichael number

2016 – triangular number, number of 5-cubes in a 9-cube, Erdős–Nicolas number, 2¹¹-2⁵.

2017 – Mertens function zero. (2011, 2017) is a sexy prime pair.

2020 – sum of the totient function for the first 81 integers

2024 – tetrahedral number

2025 – 45², sum of the cubes of the first nine integers, centered octagonal number

2027 – safe prime

2029 – member of the Mian–Chowla sequence

2030 – 21² + 22² + 23² + 24² = 25² + 26² + 27²

2031 – centered pentagonal number

2039 – Sophie Germain prime, safe prime

2047 – super-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.

2048 – power of two

2056 – magic 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

2070 – pronic 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

2101 – centered heptagonal number

2107 – member of a Ruth–Aaron pair with 2108 (first definition)

2108 – member of a Ruth–Aaron pair with 2107 (first definition)

2109 – square pyramidal number

2112 – The break-through album of the band Rush

2113 – Mertens function zero, Proth prime, centered square number

2116 – 46²

2117 – Mertens function zero

2119 – Mertens function zero

2120 – Mertens function zero

2122 – Mertens function zero

2125 – nonagonal 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

2169 – Leyland number

2171 – Mertens function zero

2172 – Mertens function zero

2175 – smallest number requiring 143 seventh powers for Waring representation

2176 – pentagonal pyramidal number, centered pentagonal number

2178 – first natural integer which digits in its decimal expression get reversed when multiplied by 4.

2179 – Wedderburn–Etherington number

2187 – 3⁷, vampire number, perfect totient number

2188 – Motzkin number

2197 – 13³, palindromic in base 12 (1331₁₂)

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

2208 – Keith number

2209 – 47², palindromic in base 14 (B3B₁₄), centered octagonal number

2211 – triangular number

2222 – repdigit

2223 – Kaprekar number

2230 – sum of the totient function for the first 85 integers

2232 – decagonal number

2236 – Harshad Number

2245 – centered square number

2254 – member of the Mian–Chowla sequence

2255 – octahedral number

2256 – pronic number

2269 – cuban 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

2287 – balanced 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 – 48²

2306 – Mertens function zero

2309 – primorial 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

2331 – centered cube number

2338 – Mertens function zero

2339 – Sophie Germain prime

2346 – triangular number

2351 – Sophie Germain prime

2352 – pronic number

2357 – Smarandache–Wellin prime

2368 – sum of the totient function for the first 88 integers

2378 – Pell number

2379 – member of the Mian–Chowla sequence

2381 – centered square number

2383 (2384) – number of delegates required to win the 2016 Democratic Party presidential primaries (out of 4051)

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 – 7⁴, 49², 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

2465 – magic 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 – 50², palindromic in base 7 (10201₇)

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)

2520 – superior 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)

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

2584 – Fibonacci 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)

2600 Hz is the tone used by a blue box to defeat toll charges on long distance telephone calls.

2600: The Hacker Quarterly is a magazine named after the above.

The Atari 2600 was a popular video game console.

2601 – 51², member of a Ruth–Aaron pair with 2600 (first definition)

2620 – amicable 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 – 52²

2719 – 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.

2728 – Kaprekar number

2729 – highly cototient number

2731 – Wagstaff prime

2736 – octahedral number

2741 – Sophie Germain prime

2744 – 14³, palindromic in base 13 (1331₁₃)

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 – 53², 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

2872 – tetranacci number

2879 – safe prime

2897 – Markov 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 – 54²

2924 – amicable number with 2620

2925 – magic 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

2970 – harmonic divisor number, pronic number

2976 – centered pentagonal number

2997 – chiliagonal number

2999 – safe prime

References

2000 (number) Wikipedia

(Text) CC BY-SA