2000 (number)

Selected numbers in the range 2001–2999

2001 to 2099

• 2001 – sphenic number
• 2002 – palindromic 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. is a sexy prime pair.
• 2019 – smallest number that can be represented as the sum of 3 prime squares 6 different ways: 2019 = 7² + 11² + 43² = 7² + 17² + 41² = 13² + 13² + 41² = 11² + 23² + 37² = 17² + 19² + 37² = 23² + 23² + 31².
• 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 – super-prime, 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 2¹¹
• 2053 – star number
• 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. super-prime
• 2069 – Sophie Germain prime
• 2070 – pronic number
• 2080 – triangular number
• 2081 – super-prime
• 2093 – Mertens function zero
• 2095 – Mertens function zero
• 2096 – Mertens function zero
• 2097 – Mertens function zero
• 2099 – Mertens function zero, super-prime, safe prime, highly cototient number

  2100 to 2199

• 2100 – Mertens function zero
• 2101 – centered heptagonal number
• 2107 – member of a Ruth–Aaron pair with 2108
• 2108 – member of a Ruth–Aaron pair with 2107
• 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
• 2137 – prime of the form 2p-1
• 2138 – Mertens function zero
• 2141 – Sophie Germain prime
• 2142 – sum of the totient function for the first 83 integers
• 2143 – almost exactly 22⁴
• 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
• 2184 – equals both 3⁷ − 3 and 13³ − 13 and is believed to be the only such doubly strictly absurd number.
• 2187 – power of three: 3⁷, vampire number, perfect totient number
• 2188 – Motzkin number
• 2197 – 13³, palindromic in base 12
• 2199 – perfect totient number

  2200 to 2299

• 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, centered octagonal number
• 2211 – triangular number
• 2221 – super-prime, happy 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 – super-prime, 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
• 2281 – star 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

  2300 to 2399

• 2300 – tetrahedral number, member of a Ruth–Aaron pair with 2299
• 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
• 2341 – super-prime, twin prime with 2339
• 2346 – triangular number
• 2347 – sum of seven consecutive primes
• 2351 – Sophie Germain prime, super-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 – super-prime, centered square number
• 2383 – number of delegates required to win the 2016 Democratic Party presidential primaries
• 2393 – Sophie Germain prime
• 2397 – sum of the squares of the first ten primes
• 2399 – Sophie Germain prime

  2400 to 2499

• 2400 – perfect score on SAT tests administered after 2005
• 2401 – 7⁴, 49², centered octagonal number
• 2415 – triangular number
• 2417 – super-prime, 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
• 2477 – super-prime, cousin prime
• 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 to 2599

• 2500 – 50², palindromic in base 7
• 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, 2, 3,..., 9
• 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. Not only is it the 7th 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 which is a property the previous number with this pattern of divisors does not have. 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 and is not divisible by 1 to 7. It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number.
• 2521 – star number, 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, super-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 to 2699

• 2600 – tetrahedral number, member of a Ruth–Aaron pair with 2601
• * 2600 Hz is the tone used by a blue box to defeat toll charges on long distance telephone calls.
• * 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
• 2609 – super-prime
• 2620 – amicable number with 2924
• 2626 – decagonal number
• 2628 – triangular number
• 2632 – number of consecutive baseball games played by Cal Ripken, Jr.
• 2633 – sum of twenty-five consecutive primes
• 2641 – centered pentagonal number
• 2647 – super-prime, 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
• 2683 – super-prime
• 2689 – Mertens function zero, Proth prime
• 2693 – Sophie Germain prime
• 2699 – Sophie Germain prime

  2700 to 2799

• 2701 – triangular number, super-Poulet number
• 2702 – sum of the totient function for the first 94 integers
• 2704 – 52²
• – super-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.
• 2728 – Kaprekar number
• 2729 – highly cototient number
• 2731 – Wagstaff prime
• 2736 – octahedral number
• 2741 – Sophie Germain prime, 400th prime number
• 2744 – 14³, palindromic in base 13
• 2747 – sum of the first 38 primes
• 2749 – super-prime, cousin prime with 2753
• 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
• 2784 – member of a Ruth–Aaron pair with 2783
• 2791 – cuban prime

  2800 to 2899

• 2801 – first base 7 repunit prime
• 2803 – super-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, sum of seven consecutive primes
• 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 – super-prime, Markov number

  2900 to 2999

• 2902 – sum of the totient function for the first 97 integers
• 2903 – Sophie Germain prime, safe prime, balanced prime
• 2909 – super-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