3000 (number)

Short description: Natural number

| <- 2999 | 3000 | 3001 ->

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List of numbers — Integers

← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →

Cardinal| three thousand
Ordinal| 3000th
(three thousandth)
Factorization| 23 × 3 × 53
Greek numeral| ,Γ´
Roman numeral| MMM
Unicode symbol(s)| MMM, mmm
Binary| 1011101110002
Ternary| 110100103
Quaternary| 2323204
Quinary| 440005
Senary| 215206
Octal| 56708
Duodecimal| 18A012
Hexadecimal| BB816
Vigesimal| 7A020
Base 36| 2BC36

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).

## Contents

* 1 Selected numbers in the range 3001–3999
* 1.1 3001 to 3099
* 1.2 3100 to 3199
* 1.3 3200 to 3299
* 1.4 3300 to 3399
* 1.5 3400 to 3499
* 1.6 3500 to 3599
* 1.7 3600 to 3699
* 1.8 3700 to 3799
* 1.9 3800 to 3899
* 1.10 3900 to 3999
* 1.11 Prime numbers
* 2 References

## 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 = 552, sum of the cubes of the first ten integers, centered octagonal number,[1] dodecagonal number[2]
* 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[3]
* 3052 – decagonal number[4]
* 3059 – centered cube number[5]
* 3061 – prime of the form 2p-1
* 3063 – perfect totient number[6]
* 3067 – super-prime
* 3071 – Thabit number
* 3072 – 3-smooth number (210×3)
* 3075 – nonagonal number[7]
* 3078 – 18th pentagonal pyramidal number[8]
* 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,[9] emirp, largest minimal prime in quinary.
* 3125 – a solution to the expression nn, where n=5 (3125=55).
* 3136 = 562, palindromic in ternary (110220113), tribonacci number[10]
* 3137 – Proth prime,[11] both a left- and right-truncatable prime
* 3149 – highly cototient number[12]
* 3155 – member of the Mian–Chowla sequence[13]
* 3160 – triangular number
* 3167 – safe prime
* 3169 – super-prime, Cuban prime of the form x=y+1.[14]
* 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[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

* 3301 – a *not* normal prime number (cicada 3301)
* 3306 – pronic number
* 3307 – balanced prime[20]
* 3313 – balanced prime, star number[20]
* 3319 – super-prime, happy number
* 3321 – triangular number
* 3329 – 86th Sophie Germain prime, Proth prime,[11] member of the Padovan sequence[21]
* 3354 – member of the Mian–Chowla sequence[13]
* 3358 – sum of the squares of the first eleven primes
* 3359 – 87th Sophie Germain prime, highly cototient number[12]
* 3363/2378 ≈ √2
* 3364 = 582
* 3367 = 153 \- 23 = 163 \- 93 = 343 \- 333[importance?]
* 3375 = 153, palindromic in base 14 (133114), 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 nn: 3413 = 11 \+ 22 \+ 33 \+ 44 \+ 55
* 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 (33 + 44 + 33 + 55 = 3435)
* 3439 – magic constant of n×n normal magic square and n-queens problem for n = 19.
* 3445 – centered square number[9]
* 3447 – sum of first 42 primes
* 3449 – 90th Sophie Germain prime
* 3456 – 3-smooth number (27×33)
* 3457 – Proth prime[11]
* 3463 – happy number
* 3467 – safe prime
* 3469 – super-prime, Cuban prime of the form x = y \+ 2, completes the tenth prime quadruplet set[22]
* 3473 – centered heptagonal number[3]
* 3481 = 592, centered octagonal number[1]
* 3486 – triangular number
* 3491 – 91st Sophie Germain prime

### 3500 to 3599

* 3504 – nonagonal number[7]
* 3510 – decagonal number[4]
* 3511 – largest known Wieferich prime
* 3512 – number of primes ≤215.[23]
* 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[12]
* 3570 – triangular number
* 3571 – 500th prime, Cuban prime of the form x = y \+ 1,[14] 17th Lucas number,[24] 4th balanced prime of order 4.[25]
* 3591 – member of the Mian–Chowla sequence[13]
* 3593 – 93rd Sophie Germain prime, super-prime

### 3600 to 3699

* 3600 = 602, number of seconds in an hour, called šār or šāru in the sexagesimal system of Ancient Mesopotamia (cf. Saros), 1201-gonal number
* 3601 – star number
* 3610 – 19th pentagonal pyramidal number[8]
* 3613 – centered square number[9]
* 3617 – sum of eleven consecutive primes (293 + 307 + 311 + 313 + 317 + 331 + 337 + 347 + 349 + 353 + 359)
* 3623 – 94th Sophie Germain prime, safe prime
* 3637 – balanced prime, super-prime[20]
* 3638 – sum of first 43 primes, 599th sphenic number
* 3643 – happy number, sum of seven consecutive primes (499 + 503 + 509 + 521 + 523 + 541 + 547)
* 3654 – tetrahedral number[17]
* 3655 – triangular number, 601st sphenic number
* 3660 – pronic number
* 3684 – 13th Keith number[26]
* 3697 – centered heptagonal number[3]

### 3700 to 3799

* 3721 = 612, centered octagonal number[1]
* 3729 – nonagonal number[7]
* 3733 – balanced prime, super-prime[20]
* 3741 – triangular number, 618th sphenic number
* 3751 – decagonal number[4]
* 3761 – 95th Sophie Germain prime, super-prime
* 3779 – 96th Sophie Germain prime, safe prime
* 3782 – pronic number, 623rd sphenic number
* 3785 – centered square number[9]
* 3797 – member of the Mian–Chowla sequence,[13] both a left- and right- truncatable prime

### 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. ↑ 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.
2. ↑ "Sloane's A051624 : 12-gonal (or dodecagonal) numbers". OEIS Foundation. https://oeis.org/A051624.
3. ↑ 3.0 3.1 3.2 3.3 3.4 "Sloane's A069099 : Centered heptagonal numbers". OEIS Foundation. https://oeis.org/A069099.
4. ↑ 4.0 4.1 4.2 4.3 "Sloane's A001107 : 10-gonal (or decagonal) numbers". OEIS Foundation. https://oeis.org/A001107.
5. ↑ 5.0 5.1 "Sloane's A005898 : Centered cube numbers". OEIS Foundation. https://oeis.org/A005898.
6. ↑ "Sloane's A082897 : Perfect totient numbers". OEIS Foundation. https://oeis.org/A082897.
7. ↑ 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. ↑ 8.0 8.1 "Sloane's A002411 : Pentagonal pyramidal numbers". OEIS Foundation. https://oeis.org/A002411.
9. ↑ 9.0 9.1 9.2 9.3 9.4 9.5 "Sloane's A001844 : Centered square numbers". OEIS Foundation. https://oeis.org/A001844.
10. ↑ "Sloane's A000073 : Tribonacci numbers". OEIS Foundation. https://oeis.org/A000073.
11. ↑ 11.0 11.1 11.2 "Sloane's A080076 : Proth primes". OEIS Foundation. https://oeis.org/A080076.
12. ↑ 12.0 12.1 12.2 12.3 "Sloane's A100827 : Highly cototient numbers". OEIS Foundation. https://oeis.org/A100827.
13. ↑ 13.0 13.1 13.2 13.3 13.4 "Sloane's A005282 : Mian-Chowla sequence". OEIS Foundation. https://oeis.org/A005282.
14. ↑ 14.0 14.1 "Sloane's A002407 : Cuban primes". OEIS Foundation. https://oeis.org/A002407.
15. ↑ 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.
16. ↑ 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. ↑ 17.0 17.1 "Sloane's A000292 : Tetrahedral numbers". OEIS Foundation. https://oeis.org/A000292.
18. ↑ "Sloane's A050217 : Super-Poulet numbers". OEIS Foundation. https://oeis.org/A050217.
19. ↑ 19.0 19.1 "Sloane's A005900 : Octahedral numbers". OEIS Foundation. https://oeis.org/A005900.
20. ↑ 20.0 20.1 20.2 20.3 "Sloane's A006562 : Balanced primes". OEIS Foundation. https://oeis.org/A006562.
21. ↑ "Sloane's A000931 : Padovan sequence". OEIS Foundation. https://oeis.org/A000931.
22. ↑ 22.0 22.1 "Sloane's A002648 : A variant of the cuban primes". OEIS Foundation. https://oeis.org/A002648.
23. ↑ Sloane, N. J. A., ed. "Sequence A007053". OEIS Foundation. https://oeis.org/A007053. Retrieved 2022-06-02.
24. ↑ "Sloane's A000032 : Lucas numbers". OEIS Foundation. https://oeis.org/A000032.
25. ↑ "Sloane's A082079 : Balanced primes of order four". OEIS Foundation. https://oeis.org/A082079.
26. ↑ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". OEIS Foundation. https://oeis.org/A007629.
27. ↑ 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.
28. ↑ 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.
29. ↑ Sloane, N. J. A., ed. "Sequence A046528". OEIS Foundation. https://oeis.org/A046528.
30. ↑ Sloane, N. J. A., ed. "Sequence A247838". OEIS Foundation. https://oeis.org/A247838.
31. ↑ Lamb, Evelyn (October 25, 2019), "Farewell to the Fractional Foot", Scientific American, https://blogs.scientificamerican.com/roots-of-unity/farewell-to-the-fractional-foot/
32. ↑ Sloane, N. J. A., ed. "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". OEIS Foundation. https://oeis.org/A038823.
33. ↑ 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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