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3000 (number)

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Natural number

← 2999

3000

3001 →

←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,mmm

Unicode symbol(s)

MMM, mmm

101110111000₂

11010010₃

21520₆

5670₈

18A0₁₂

BB8₁₆

𓆾

3000 (three thousand) is thenatural number following2999 and preceding3001. It is the smallest number requiring thirteen letters in English (when "and" is required from 101 forward).

Selected numbers in the range 3001–3999

[edit]

3001 to 3099

[edit]

3001 –super-prime; divides theEuclid number 2999# + 1
3003 –triangular number, only number known to appear eight times inPascal's triangle; no number is known to appear more than eight times other than 1. (seeSingmaster's conjecture)
3019 –super-prime,happy prime
3023 – 84thSophie Germain prime, 51stsafe 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 210and 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 – 18thpentagonal pyramidal number^[8]
3080 –pronic number
3081 – triangular number, 497thsphenic number
3087 – sum of first 40 primes

3100 to 3199

[edit]

3109 –super-prime
3119 –safe prime
3121 –centered square number,^[9]emirp, largestminimal prime inquinary.
3125 – a solution to the expression $n^{n}$ , where $n=5$ ( $3125=5^{5}$ ).
3136 = 56², palindromic internary (11022011₃),tribonacci number^[10]
3137 –Proth prime,^[11] both a left- and right-truncatable prime
3149 –highly cototient number^[12]
3150 = 15³ - 15²
3155 – member of theMian–Chowla sequence^[13]
3159 = number of trees with 14 unlabeled nodes^[14]
3160 –triangular number
3167 – safe prime
3169 –super-prime,Cuban prime of the form $x=y+1$ .^[15]
3192 –pronic number

3200 to 3299

[edit]

3203 – safe prime
3207 – number of compositions of 14 whose run-lengths are either weakly increasing or weakly decreasing^[16]
3229 –super-prime
3240 –triangular number
3248 – member of aRuth-Aaron pair with 3249 under second definition, largest number whosefactorial 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 ninthprime quadruplet set
3264 – solution toSteiner's conic problem: number of smooth conics tangent to 5 given conics in general position^[17]
3266 – sum of first 41 primes, 523rdsphenic number
3276 –tetrahedral number^[18]
3277 – 5thsuper-Poulet number,^[19] decagonal number^[4]
3279 – first compositeWieferich number
3281 –octahedral number,^[20] centered square number^[9]
3286 – nonagonal number^[7]
3299 – 85thSophie Germain prime, super-prime

3300 to 3399

[edit]

3306 –pronic number
3307 –balanced prime^[21]
3313 – balanced prime,star number^[21]
3319 –super-prime,happy number
3321 –triangular number
3329 – 86thSophie Germain prime, Proth prime,^[11] member of thePadovan sequence^[22]
3354 – member of the Mian–Chowla sequence^[13]
3358 – sum of the squares of the first eleven primes
3359 – 87thSophie Germain prime,highly cototient number^[12]
3360 – largely composite number^[23]
3363/2378 ≈√2
3364 = 58²
3367 = 15³ - 2³ = 16³ - 9³ = 34³ - 33³^{[importance?]}
3375 = 15³, palindromic in base 14 (1331₁₄), 15thcube
3389 – 88thSophie Germain prime

3400 to 3499

[edit]

3403 –triangular number
3407 –super-prime
3413 – 89thSophie Germain prime, sum of the first 5 nⁿ: 3413 = 1¹ + 2² + 3³ + 4⁴ + 5⁵
3422 –pronic number, 553rdsphenic number,melting point oftungsten indegrees Celsius
3435 – aperfect digit-to-digit invariant, equal to the sum of its digits to their own powers (3³ + 4⁴ + 3³ + 5⁵ = 3435)
3439 –magic constant ofn×n normalmagic square andn-queens problem forn = 19.
3445 –centered square number^[9]
3447 – sum of first 42 primes
3449 – 90thSophie 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 formx =y + 2, completes the tenthprime quadruplet set^[24]
3473 – centered heptagonal number^[3]
3481 = 59², centered octagonal number^[1]
3486 – triangular number
3491 – 91stSophie Germain prime

3500 to 3599

[edit]

3504 – nonagonal number^[7]
3510 – decagonal number^[4]
3511 – largest knownWieferich prime
3512 – number of primes $\leq 2^{15}$ .^[25]
3517 –super-prime, sum of nine consecutive primes (367 + 373 + 379 + 383 + 389 + 397 + 401 + 409 + 419)
3539 – 92ndSophie Germain prime
3540 –pronic number
3559 –super-prime
3569 –highly cototient number^[12]
3570 –triangular number
3571 – 500th prime,Cuban prime of the formx =y + 1,^[15] 17thLucas number,^[26] 4thbalanced prime of order 4.^[27]
3591 – member of the Mian–Chowla sequence^[13]
3593 – 93rdSophie Germain prime, super-prime

3600 to 3699

[edit]

3600 = 60², number ofseconds in anhour, calledšār oršāru in thesexagesimal system ofAncient Mesopotamia (cf.Saros), 1201-gonal number
3601 –star number
3610 – 19thpentagonal 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 – 94thSophie Germain prime, safe prime
3637 – balanced prime,super-prime^[21]
3638 – sum of first 43 primes, 599thsphenic number
3643 –happy number, sum of seven consecutive primes (499 + 503 + 509 + 521 + 523 + 541 + 547)
3654 –tetrahedral number^[18]
3655 –triangular number, 601stsphenic number
3660 –pronic number
3684 – 13thKeith number^[28]
3697 – centered heptagonal number^[3]

3700 to 3799

[edit]

3721 = 61², centeredoctagonal number^[1]
3729 – nonagonal number^[7]
3733 – balanced prime,super-prime^[21]
3741 –triangular number, 618thsphenic number
3751 – decagonal number^[4]
3761 – 95thSophie Germain prime, super-prime
3779 – 96thSophie Germain prime, safe prime
3780 – largely composite number^[23]
3782 –pronic number, 623rdsphenic number
3785 –centered square number^[9]
3797 – member of the Mian–Chowla sequence,^[13] both a left- and right-truncatable prime

3800 to 3899

[edit]

3803 – 97thSophie Germain prime,safe prime, the largest prime factor of 123,456,789
3821 – 98thSophie Germain prime
3828 –triangular number
3831 – sum of first 44 primes
3840 = 16³ - 16²,double factorial of 10
3844 = 62²
3851 – 99thSophie 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^[29]
3863 – 100thSophie Germain prime
3865 – greater of third pair ofSmith brothers
3888 – longest number when expressed inRoman numerals I, V, X, L, C, D, and M (MMMDCCCLXXXVIII),3-smooth number (2⁴×3⁵)
3889 –Cuban prime of the formx =y + 2^[24]
3894 –octahedral number^[20]

3900 to 3999

[edit]

3901 –star number
3906 –pronic number
3911 – 101stSophie Germain prime,super-prime
3914 – number of 18-bead necklaces (turning over is allowed) where complements are equivalent^[30]
3916 –triangular number
3925 – centered cube number^[5]
3926 – 12thopen meandric number, 654thsphenic number
3928 – centered heptagonal number^[3]
3937 – product of distinct Mersenne primes,^[31] repeated sum of divisors is prime,^[32] denominator of conversion factor from meter toUS survey foot^[33]
3940 – there are 3940 distinct ways to arrange the 12 flatpentacubes (or 3-Dpentominoes) into a 3x4x5 box (not counting rotations and reflections)
3943 –super-prime
3947 – safe prime
3960 – largely composite number^[23]
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 usingRoman numerals I, V, X, L, C, D, and M (MMMCMXCIX), ignoringvinculum

Prime numbers

[edit]

There are 120prime numbers between 3000 and 4000:^[34]^[35]

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

[edit]

^^a ^b ^c ^d ^eSloane, N. J. A. (ed.)."Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A051624 (12-gonal (or dodecagonal) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^eSloane, N. J. A. (ed.)."Sequence A069099 (Centered heptagonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^dSloane, N. J. A. (ed.)."Sequence A001107 (10-gonal (or decagonal) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A005898 (Centered cube numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A082897 (Perfect totient numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^eSloane, N. J. A. (ed.)."Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A002411 (Pentagonal pyramidal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^e ^fSloane, N. J. A. (ed.)."Sequence A001844 (Centered square numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000073 (Tribonacci numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^cSloane, N. J. A. (ed.)."Sequence A080076 (Proth primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^dSloane, N. J. A. (ed.)."Sequence A100827 (Highly cototient numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^d ^eSloane, N. J. A. (ed.)."Sequence A005282 (Mian-Chowla sequence)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000055 (Number of trees with n unlabeled nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A002407 (Cuban primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Bashelor, Andrew; Ksir, Amy; Traves, Will (2008),"Enumerative algebraic geometry of conics."(PDF),Amer. Math. Monthly,115 (8):701–728,doi:10.1080/00029890.2008.11920584,JSTOR 27642583,MR 2456094,S2CID 16822027
^^a ^bSloane, N. J. A. (ed.)."Sequence A000292 (Tetrahedral numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A050217 (Super-Poulet numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A005900 (Octahedral numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^c ^dSloane, N. J. A. (ed.)."Sequence A006562 (Balanced primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000931 (Padovan sequence)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^b ^cSloane, N. J. A. (ed.)."Sequence A067128 (Ramanujan's largely composite numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^^a ^bSloane, N. J. A. (ed.)."Sequence A002648 (A variant of the cuban primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A007053 (Number of primes <= 2^n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000032 (Lucas numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A082079 (Balanced primes of order four)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^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)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A046528 (Numbers that are a product of distinct Mersenne primes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A247838 (Numbers n such that sigma(sigma(n)) is prime)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Lamb, Evelyn (October 25, 2019),"Farewell to the Fractional Foot", Roots of Unity,Scientific American
^Sloane, N. J. A. (ed.)."Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Stein, William A. (10 February 2017)."The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture".wstein.org. Retrieved6 February 2021.

\mathbb {Z}

Integers

−2,−1

0 to 199

0 to 99	100 to 199
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99	100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

200 to 399

200 to 299	300 to 399
200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299	300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399

400 to 999

400s, 500s, and 600s	700s, 800s, and 900s
400 420 440 495 496 500 501 511 512 555 600 610 613 616 666 693	700 720 743 744 777 786 800 801 836 840 880 881 888 900 911 971 987 999

1000s and 10,000s
1000s	1000 1001 1023 1024 1089 1093 1105 1234 1289 1458 1510 1728 1729 1980 1987 2000 2016 2520 3000 3511 4000 4104 5000 5040 6000 6174 7000 7744 7825 8000 8128 8192 9000 9855 9999
10,000s	10,000 16,807 20,000 30,000 40,000 50,000 60,000 64,079 65,535 65,536 65,537 70,000 80,000 90,000

100,000s to 10,000,000,000,000s
100,000 142,857 144,000 1,000,000 10,000,000 43,112,609 100,000,000 1,000,000,000 2,147,483,647 4,294,967,295 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000

Large numbers

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