3000 (number)
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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).
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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 | |||
Octal | 56708 | |||
Duodecimal | 18A012 | |||
Hexadecimal | BB816 |
Selected numbers in the range 3001–3999Edit
3001 to 3099Edit
- 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 number
- 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, prime number mentioned in a question during a quiz in Little Man Tate, where it was asked what its factors were, and the response was that it has none, since it is indeed Prime.
- 3071 – Thabit number
- 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 3199Edit
- 3109 – super-prime
- 3119 – safe prime
- 3121 – centered square number,[9] emirp
- 3125 – 55
- 3136 – 562, palindromic in base 3 (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 3299Edit
- 3203 – safe prime
- 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[15]
- 3266 – sum of first 41 primes, 523rd sphenic number
- 3276 – tetrahedral number[16]
- 3277 – 5th super-Poulet number,[17] decagonal number[4]
- 3281 – octahedral number,[18] centered square number[9]
- 3286 – nonagonal number[7]
- 3299 – 85th Sophie Germain prime, super-prime
3300 to 3399Edit
- 3301 – a normal prime number
- 3306 – pronic number
- 3307 – balanced prime[19]
- 3313 – balanced prime, star number[19]
- 3319 – super-prime, happy number
- 3321 – triangular number
- 3329 – 86th Sophie Germain prime, Proth prime,[11] member of the Padovan sequence[20]
- 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]
- 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 3499Edit
- 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
- 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[21]
- 3473 – centered heptagonal number[3]
- 3481 – 592, centered octagonal number[1]
- 3486 – triangular number
- 3491 – 91st Sophie Germain prime
3500 to 3599Edit
- 3504 – nonagonal number[7]
- 3510 – decagonal number[4]
- 3511 – largest known Wieferich prime
- 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,[22] 4th balanced prime of order 4.[23]
- 3591 – member of the Mian–Chowla sequence[13]
- 3593 – 93rd Sophie Germain prime, super-prime
3600 to 3699Edit
- 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[19]
- 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[16]
- 3655 – triangular number, 601st sphenic number
- 3660 – pronic number
- 3684 – 13th Keith number[24]
- 3697 – centered heptagonal number[3]
3700 to 3799Edit
- 3721 – 612, centered octagonal number[1]
- 3729 – nonagonal number[7]
- 3733 – balanced prime, super-prime[19]
- 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 3899Edit
- 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
- 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)
- 3889 – Cuban prime of the form x = y + 2[21]
- 3894 – octahedral number[18]
3900 to 3999Edit
- 3901 – star number
- 3906 – pronic number
- 3911 – 101st Sophie Germain prime, super-prime
- 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,[25] repeated sum of divisors is prime,[26] denominator of conversion factor from meter to US survey foot[27]
- 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]
- 3967 – Carol number[28]
- 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
ReferencesEdit
- ^ a b c d e "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A051624 : 12-gonal (or dodecagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c d e "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c d "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c d e "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c d e f "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c d "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c d e "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ Bashelor, Andrew; Ksir, Amy; Traves, Will (2008), "Enumerative algebraic geometry of conics." (PDF), Amer. Math. Monthly, 115 (8): 701–728, JSTOR 27642583, MR 2456094
- ^ a b "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ a b c d "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ a b "Sloane's A002648 : A variant of the cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A000032 : Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A082079 : Balanced primes of order four". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
- ^ Sloane, N. J. A. (ed.). "Sequence A046528". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A247838". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Lamb, Evelyn (October 25, 2019), "Farewell to the Fractional Foot", Roots of Unity, Scientific American
- ^ "Sloane's A093112 : a(n) = (2^n-1)^2 - 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.