2000 (number)

Factors

The factors of 2000 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000 and 2000.

Multiples

Here are the first 10 multiples of 2000:

And the 20 multiples:

2001 to 2099

2100 to 2199

2200 to 2299

2300 to 2399

2400 to 2499

• 2401 = 49² = 7⁴, centered octagonal number
• 2415 – triangular number
• 2417 – super-prime, balanced prime
• 2425 – decagonal number
• 2437 – cuban prime, largest right-truncatable prime in base 5
• 2447 – safe prime
• 2450 – pronic number
• 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
• 2481 – centered pentagonal number
• 2484 – nonagonal number
• 2485 – triangular number, number of planar partitions of 13
• 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

• 2510 – member of the Mian–Chowla sequence
• 2513 – member of the Padovan sequence
• 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 it is the 7th (and last) number with more divisors than any number double itself but is 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 – star prime, centered square number
• 2530 – Leyland number
• 2543 – Sophie Germain prime, sexy prime with 2549
• 2549 – Sophie Germain prime, super-prime, sexy prime with 2543
• 2550 – pronic number
• 2556 – triangular number
• 2579 – safe prime, palindromic prime in bases 5, 25, and 28: 2579 = 40304₅ = 434₂₅ = 383₂₈
• 2580 – Keith number,
• 2584 – Fibonacci number,

2600 to 2699

• 2600 – tetrahedral number, member of a Ruth–Aaron pair with 2601 (first definition)
• 2601 = 51², member of a Ruth–Aaron pair with 2600 (first definition)
• 2609 – super-prime
• 2620 – telephone number, amicable number with 2924
• 2625 = a centered octahedral number
• 2626 – decagonal number
• 2628 – triangular number
• 2641 – centered pentagonal number
• 2647 – super-prime, centered heptagonal number
• 2652 – pronic number
• 2665 – centered square number
• 2674 – nonagonal number
• 2677 – balanced prime
• 2680 – number of 11-queens problem solutions
• 2683 – super-prime
• 2689 – 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
• 2707 – strong prime
• 2719 – 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^[when?] known this is true if the generalized Riemann hypothesis is true.
• 2728 – Kaprekar number
• 2729 – highly cototient number
• 2731 – the only Wagstaff prime with four digits, Jacobsthal prime
• 2736 – octahedral number
• 2741 – Sophie Germain prime, 400th prime number
• 2744 = 14³, palindromic in base 13 (1331₁₃)
• 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 (first definition)
• 2784 – member of a Ruth–Aaron pair with 2783 (first definition)
• 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 (383 + 389 + 397 + 401 + 409 + 419 + 421)
• 2821 – Carmichael number
• 2835 – decagonal number
• 2843 – centered heptagonal prime
• 2850 – triangular number
• 2862 – pronic number
• 2870 – square pyramidal number
• 2871 – nonagonal number
• 2872 – tetranacci number
• 2875 – number of lines on a quintic threefold
• 2879 – safe prime
• 2897 – super-prime, Markov prime

2900 to 2999

• 2903 – Sophie Germain prime, safe prime, balanced prime
• 2909 – super-prime
• 2915 – Lucas–Carmichael number
• 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
• 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
• 2999 – safe 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