3000 (three thousand) is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English (when "and" is required from 101 forward).
Selected numbers in the range 3001–3999
3001 to 3099
- 3001 – super-prime; divides the Euclid number 2999# + 1
- 3003 – triangular number, only number known to appear eight times in Pascal's triangle; no number is known to appear more than eight times other than 1. (see Singmaster's conjecture)
- 3019 – super-prime, happy prime
- 3023 – 84th Sophie Germain prime, 51st safe prime
- 3025 = 55<sup>2</sup>, sum of the cubes of the first ten integers, centered octagonal number, dodecagonal number
- 3037 – star number, cousin prime with 3041
- 3045 – sum of the integers 196 to 210 and sum of the integers 211 to 224
- 3046 – centered heptagonal number
- 3052 – decagonal number
- 3059 – centered cube number
- 3061 – prime of the form 2p-1
- 3063 – perfect totient number
- 3067 – super-prime
- 3071 – Thabit number
- 3072 – 3-smooth number (2<sup>10</sup>×3)
- 3075 – nonagonal number
- 3078 – 18th pentagonal pyramidal number
- 3080 – pronic number
- 3081 – triangular number, 497th sphenic number
- 3087 – sum of first 40 primes
3100 to 3199
- 3109 – super-prime
- 3119 – safe prime
- 3121 – centered square number, emirp, largest minimal prime in quinary.
- 3125 – a solution to the expression <math>n^n</math>, where <math>n=5</math> (<math>3125=5^5</math>).
- 3136 = 56<sup>2</sup>, palindromic in ternary (11022011<sub>3</sub>), tribonacci number
- 3137 – Proth prime, both a left- and right-truncatable prime
- 3149 – highly cototient number
- 3150 = 15<sup>3</sup> - 15<sup>2</sup>
- 3155 – member of the Mian–Chowla sequence
- 3159 = number of trees with 14 unlabeled nodes
- 3160 – triangular number
- 3167 – safe prime
- 3169 – super-prime, Cuban prime of the form <math>x=y+1</math>.
- 3192 – pronic number
3200 to 3299
- 3203 – safe prime
- 3207 – number of compositions of 14 whose run-lengths are either weakly increasing or weakly decreasing
- 3229 – super-prime
- 3240 – triangular number
- 3248 – member of a Ruth-Aaron pair with 3249 under second definition, largest number whose factorial is less than 10<sup>10000</sup> – hence its factorial is the largest certain advanced computer programs can handle.
- 3249 = 57<sup>2</sup>, palindromic in base 7 (12321<sub>7</sub>), centered octagonal number,
- 3266 – sum of first 41 primes, 523rd sphenic number
- 3276 – tetrahedral number
- 3277 – 5th super-Poulet number, decagonal number centered square number
- 3313 – balanced prime, star number
- 3354 – member of the Mian–Chowla sequence
- 3363/2378 ≈ √2
- 3364 = 58<sup>2</sup>
- 3367 = 15<sup>3</sup> - 2<sup>3</sup> = 16<sup>3</sup> - 9<sup>3</sup> = 34<sup>3</sup> - 33<sup>3</sup>
- 3375 = 15<sup>3</sup>, palindromic in base 14 (1331<sub>14</sub>), 15th cube
- 3389 – 88th Sophie Germain prime
3400 to 3499
- 3403 – triangular number
- 3407 – super-prime
- 3413 – 89th Sophie Germain prime, sum of the first 5 n<sup>n</sup>: 3413 = 1<sup>1</sup> + 2<sup>2</sup> + 3<sup>3</sup> + 4<sup>4</sup> + 5<sup>5</sup>
- 3422 – pronic number, 553rd sphenic number, melting point of tungsten in degrees Celsius
- 3435 – a perfect digit-to-digit invariant, equal to the sum of its digits to their own powers (3<sup>3</sup> + 4<sup>4</sup> + 3<sup>3</sup> + 5<sup>5</sup> = 3435)
- 3439 – magic constant of n×n normal magic square and n-queens problem for n = 19.
- 3445 – centered square number
- 3473 – centered heptagonal number
- 3517 – super-prime, sum of nine consecutive primes (367 + 373 + 379 + 383 + 389 + 397 + 401 + 409 + 419)
- 3539 – 92nd Sophie Germain prime
- 3540 – pronic number
- 3559 – super-prime
- 3569 – highly cototient number 4th balanced prime of order 4.
- 3591 – member of the Mian–Chowla sequence
- 3697 – centered heptagonal number
- 3782 – pronic number, 623rd sphenic number
- 3785 – centered square number
- 3863 – 100th Sophie Germain prime
- 3865 – greater of third pair of Smith brothers
- 3888 – longest number when expressed in Roman numerals I, V, X, L, C, D, and M (MMMDCCCLXXXVIII), 3-smooth number (2<sup>4</sup>×3<sup>5</sup>)
- 3889 – Cuban prime of the form x = y + 2
- 3916 – triangular number
- 3925 – centered cube number repeated sum of divisors is prime, denominator of conversion factor from meter to US survey foot
- 3940 – there are 3940 distinct ways to arrange the 12 flat pentacubes (or 3-D pentominoes) into a 3x4x5 box (not counting rotations and reflections)
- 3943 – super-prime
- 3947 – safe prime
- 3960 – largely composite number
- 3961 – nonagonal number,: 63<sup>2</sup> − 2 = 3,967
- 3969 = 63<sup>2</sup>, centered octagonal number
:3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989