Short description: Natural number
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
3100 to 3199
3200 to 3299
- 3203 – safe prime
- 3207 – number of compositions of 14 whose run-lengths are either weakly increasing or weakly decreasing[15]
- 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 1010000 – hence its factorial is the largest certain advanced computer programs can handle.
- 3249 = 572, palindromic in base 7 (123217), centered octagonal number,[1] member of a Ruth–Aaron pair with 3248 under second definition
- 3253 – sum of eleven consecutive primes (269 + 271 + 277 + 281 + 283 + 293 + 307 + 311 + 313 + 317 + 331)
- 3256 – centered heptagonal number[3]
- 3259 – super-prime, completes the ninth prime quadruplet set
- 3264 – solution to Steiner's conic problem: number of smooth conics tangent to 5 given conics in general position[16]
- 3266 – sum of first 41 primes, 523rd sphenic number
- 3276 – tetrahedral number[17]
- 3277 – 5th super-Poulet number,[18] decagonal number[4]
- 3281 – octahedral number,[19] centered square number[9]
- 3286 – nonagonal number[7]
- 3299 – 85th Sophie Germain prime, super-prime
3300 to 3399
3400 to 3499
3500 to 3599
3600 to 3699
3700 to 3799
3800 to 3899
- 3803 – 97th Sophie Germain prime, safe prime, the largest prime factor of 123,456,789
- 3821 – 98th Sophie Germain prime
- 3828 – triangular number
- 3831 – sum of first 44 primes
- 3844 = 622
- 3851 – 99th Sophie Germain prime
- 3856 – number of 17-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[27]
- 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 (24×35)
- 3889 – Cuban prime of the form x = y + 2[22]
- 3894 – octahedral number[19]
3900 to 3999
- 3901 – star number
- 3906 – pronic number
- 3911 – 101st Sophie Germain prime, super-prime
- 3914 – number of 18-bead necklaces (turning over is allowed) where complements are equivalent[28]
- 3916 – triangular number
- 3925 – centered cube number[5]
- 3926 – 12th open meandric number, 654th sphenic number
- 3928 – centered heptagonal number[3]
- 3937 – product of distinct Mersenne primes,[29] repeated sum of divisors is prime,[30] denominator of conversion factor from meter to US survey foot[31]
- 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
- 3961 – nonagonal number,[7] centered square number[9]
- 3969 = 632, centered octagonal number[1]
- 3989 – highly cototient number[12]
- 3998 – member of the Mian–Chowla sequence[13]
- 3999 – largest number properly expressible using Roman numerals I, V, X, L, C, D, and M (MMMCMXCIX), ignoring vinculum
Prime numbers
There are 120 prime numbers between 3000 and 4000:[32][33]
- 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
References
- ↑ 1.0 1.1 1.2 1.3 1.4 "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". OEIS Foundation. https://oeis.org/A016754.
- ↑ "Sloane's A051624 : 12-gonal (or dodecagonal) numbers". OEIS Foundation. https://oeis.org/A051624.
- ↑ 3.0 3.1 3.2 3.3 3.4 "Sloane's A069099 : Centered heptagonal numbers". OEIS Foundation. https://oeis.org/A069099.
- ↑ 4.0 4.1 4.2 4.3 "Sloane's A001107 : 10-gonal (or decagonal) numbers". OEIS Foundation. https://oeis.org/A001107.
- ↑ 5.0 5.1 "Sloane's A005898 : Centered cube numbers". OEIS Foundation. https://oeis.org/A005898.
- ↑ "Sloane's A082897 : Perfect totient numbers". OEIS Foundation. https://oeis.org/A082897.
- ↑ 7.0 7.1 7.2 7.3 7.4 "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". OEIS Foundation. https://oeis.org/A001106.
- ↑ 8.0 8.1 "Sloane's A002411 : Pentagonal pyramidal numbers". OEIS Foundation. https://oeis.org/A002411.
- ↑ 9.0 9.1 9.2 9.3 9.4 9.5 "Sloane's A001844 : Centered square numbers". OEIS Foundation. https://oeis.org/A001844.
- ↑ "Sloane's A000073 : Tribonacci numbers". OEIS Foundation. https://oeis.org/A000073.
- ↑ 11.0 11.1 11.2 "Sloane's A080076 : Proth primes". OEIS Foundation. https://oeis.org/A080076.
- ↑ 12.0 12.1 12.2 12.3 "Sloane's A100827 : Highly cototient numbers". OEIS Foundation. https://oeis.org/A100827.
- ↑ 13.0 13.1 13.2 13.3 13.4 "Sloane's A005282 : Mian-Chowla sequence". OEIS Foundation. https://oeis.org/A005282.
- ↑ 14.0 14.1 "Sloane's A002407 : Cuban primes". OEIS Foundation. https://oeis.org/A002407.
- ↑ Sloane, N. J. A., ed. "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". OEIS Foundation. https://oeis.org/A332835. Retrieved 2022-06-02.
- ↑ Bashelor, Andrew; Ksir, Amy; Traves, Will (2008), "Enumerative algebraic geometry of conics.", Amer. Math. Monthly 115 (8): 701–728, doi:10.1080/00029890.2008.11920584, https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Bashelor.pdf
- ↑ 17.0 17.1 "Sloane's A000292 : Tetrahedral numbers". OEIS Foundation. https://oeis.org/A000292.
- ↑ "Sloane's A050217 : Super-Poulet numbers". OEIS Foundation. https://oeis.org/A050217.
- ↑ 19.0 19.1 "Sloane's A005900 : Octahedral numbers". OEIS Foundation. https://oeis.org/A005900.
- ↑ 20.0 20.1 20.2 20.3 "Sloane's A006562 : Balanced primes". OEIS Foundation. https://oeis.org/A006562.
- ↑ "Sloane's A000931 : Padovan sequence". OEIS Foundation. https://oeis.org/A000931.
- ↑ 22.0 22.1 "Sloane's A002648 : A variant of the cuban primes". OEIS Foundation. https://oeis.org/A002648.
- ↑ Sloane, N. J. A., ed. "Sequence A007053". OEIS Foundation. https://oeis.org/A007053. Retrieved 2022-06-02.
- ↑ "Sloane's A000032 : Lucas numbers". OEIS Foundation. https://oeis.org/A000032.
- ↑ "Sloane's A082079 : Balanced primes of order four". OEIS Foundation. https://oeis.org/A082079.
- ↑ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". OEIS Foundation. https://oeis.org/A007629.
- ↑ Sloane, N. J. A., ed. "Sequence A000013 (Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)". OEIS Foundation. https://oeis.org/A000013.
- ↑ Sloane, N. J. A., ed. "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". OEIS Foundation. https://oeis.org/A000011.
- ↑ Sloane, N. J. A., ed. "Sequence A046528". OEIS Foundation. https://oeis.org/A046528.
- ↑ Sloane, N. J. A., ed. "Sequence A247838". OEIS Foundation. https://oeis.org/A247838.
- ↑ Lamb, Evelyn (October 25, 2019), "Farewell to the Fractional Foot", Scientific American, https://blogs.scientificamerican.com/roots-of-unity/farewell-to-the-fractional-foot/
- ↑ Sloane, N. J. A., ed. "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". OEIS Foundation. https://oeis.org/A038823.
- ↑ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/.
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