3000 (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

• 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,<ref name=":0">Template:Cite OEIS</ref> dodecagonal number<ref>Template:Cite OEIS</ref>
• 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<ref name=":1">Template:Cite OEIS</ref>
• 3052 – decagonal number<ref name=":2">Template:Cite OEIS</ref>
• 3059 – centered cube number<ref name=":3">Template:Cite OEIS</ref>
• 3061 – prime of the form 2p-1
• 3063 – perfect totient number<ref>Template:Cite OEIS</ref>
• 3067 – super-prime
• 3071 – Thabit number
• 3072 – 3-smooth number (2¹⁰×3)
• 3075 – nonagonal number<ref name=":4">Template:Cite OEIS</ref>
• 3078 – 18th pentagonal pyramidal number<ref name=":5">Template:Cite OEIS</ref>
• 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,<ref name=":6">Template:Cite OEIS</ref> 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 = 56², palindromic in ternary (11022011₃), tribonacci number<ref>Template:Cite OEIS</ref>
• 3137 – Proth prime,<ref name=":7">Template:Cite OEIS</ref> both a left- and right-truncatable prime
• 3149 – highly cototient number<ref name=":8">Template:Cite OEIS</ref>
• 3150 = 15³ - 15²
• 3155 – member of the Mian–Chowla sequence<ref name=":9">Template:Cite OEIS</ref>
• 3159 = number of trees with 14 unlabeled nodes<ref>Template:Cite OEIS</ref>
• 3160 – triangular number
• 3167 – safe prime
• 3169 – super-prime, Cuban prime of the form <math>x=y+1</math>.<ref name=":10">Template:Cite OEIS</ref>
• 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<ref>Template:Cite OEIS</ref>
• 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,<ref name=":0" /> 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<ref name=":1" />
• 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<ref>Template:Citation</ref>
• 3266 – sum of first 41 primes, 523rd sphenic number
• 3276 – tetrahedral number<ref name=":11">Template:Cite OEIS</ref>
• 3277 – 5th super-Poulet number,<ref>Template:Cite OEIS</ref> decagonal number<ref name=":2" />
• 3279 – first composite Wieferich number
• 3281 – octahedral number,<ref name=":12">Template:Cite OEIS</ref> centered square number<ref name=":6" />
• 3286 – nonagonal number<ref name=":4" />
• 3299 – 85th Sophie Germain prime, super-prime

3300 to 3399

• 3306 – pronic number
• 3307 – balanced prime<ref name=":13">Template:Cite OEIS</ref>
• 3313 – balanced prime, star number<ref name=":13" />
• 3319 – super-prime, happy number
• 3321 – triangular number
• 3329 – 86th Sophie Germain prime, Proth prime,<ref name=":7" /> member of the Padovan sequence<ref>Template:Cite OEIS</ref>
• 3354 – member of the Mian–Chowla sequence<ref name=":9" />
• 3358 – sum of the squares of the first eleven primes
• 3359 – 87th Sophie Germain prime, highly cototient number<ref name=":8" />
• 3360 – largely composite number<ref name="OEIS-A067128">Template:Cite OEIS</ref>
• 3363/2378 ≈ √2
• 3364 = 58²
• 3367 = 15³ - 2³ = 16³ - 9³ = 34³ - 33³Template:Importance inline
• 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<ref name=":6" />
• 3447 – sum of first 42 primes
• 3449 – 90th Sophie Germain prime
• 3456 – 3-smooth number (2⁷×3³)
• 3457 – Proth prime<ref name=":7" />
• 3463 – happy number
• 3467 – safe prime
• 3469 – super-prime, Cuban prime of the form x = y + 2, completes the tenth prime quadruplet set<ref name=":14">Template:Cite OEIS</ref>
• 3473 – centered heptagonal number<ref name=":1" />
• 3481 = 59², centered octagonal number<ref name=":0" />
• 3486 – triangular number
• 3491 – 91st Sophie Germain prime

3500 to 3599

• 3504 – nonagonal number<ref name=":4" />
• 3510 – decagonal number<ref name=":2" />
• 3511 – largest known Wieferich prime
• 3512 – number of primes <math>\leq 2^{15}</math>.<ref>Template:Cite OEIS</ref>
• 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<ref name=":8" />
• 3570 – triangular number
• 3571 – 500th prime, Cuban prime of the form x = y + 1,<ref name=":10" /> 17th Lucas number,<ref>Template:Cite OEIS</ref> 4th balanced prime of order 4.<ref>Template:Cite OEIS</ref>
• 3591 – member of the Mian–Chowla sequence<ref name=":9" />
• 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<ref name=":5" />
• 3613 – centered square number<ref name=":6" />
• 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<ref name=":13" />
• 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<ref name=":11" />
• 3655 – triangular number, 601st sphenic number
• 3660 – pronic number
• 3684 – 13th Keith number<ref>Template:Cite OEIS</ref>
• 3697 – centered heptagonal number<ref name=":1" />

3700 to 3799

• 3721 = 61², centered octagonal number<ref name=":0" />
• 3729 – nonagonal number<ref name=":4" />
• 3733 – balanced prime, super-prime<ref name=":13" />
• 3741 – triangular number, 618th sphenic number
• 3751 – decagonal number<ref name=":2" />
• 3761 – 95th Sophie Germain prime, super-prime
• 3779 – 96th Sophie Germain prime, safe prime
• 3780 – largely composite number<ref name="OEIS-A067128">Template:Cite OEIS</ref>
• 3782 – pronic number, 623rd sphenic number
• 3785 – centered square number<ref name=":6" />
• 3797 – member of the Mian–Chowla sequence,<ref name=":9" /> 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
• 3840 = 16³ - 16², double factorial of 10
• 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<ref>Template:Cite OEIS</ref>
• 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<ref name=":14" />
• 3894 – octahedral number<ref name=":12" />

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<ref>Template:Cite OEIS</ref>
• 3916 – triangular number
• 3925 – centered cube number<ref name=":3" />
• 3926 – 12th open meandric number, 654th sphenic number
• 3928 – centered heptagonal number<ref name=":1" />
• 3937 – product of distinct Mersenne primes,<ref>Template:Cite OEIS</ref> repeated sum of divisors is prime,<ref>Template:Cite OEIS</ref> denominator of conversion factor from meter to US survey foot<ref>Template:Citation</ref>
• 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<ref name="OEIS-A067128">Template:Cite OEIS</ref>
• 3961 – nonagonal number,<ref name=":4" /> centered square number<ref name=":6" />
• 3969 = 63², centered octagonal number<ref name=":0" />
• 3989 – highly cototient number<ref name=":8" />
• 3998 – member of the Mian–Chowla sequence<ref name=":9" />
• 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:<ref>Template:Cite OEIS</ref><ref>Template:Cite web</ref>

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