3000 (number)

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

Selected numbers in the range 3001–3999

3001 – super-prime; divides the Euclid number 2999# + 13003 – 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. 3019 – super-prime, happy prime3023 – 84th Sophie Germain prime, 51st safe prime3025 = 55², sum of the cubes of the first ten integers, centered octagonal number, dodecagonal number3037 – star number, cousin prime with 30413045 – sum of the integers 196 to 210 and sum of the integers 211 to 2243046 – centered heptagonal number3052 – decagonal number3059 – cube number">Cube (arithmetic)">cube number3061 – prime of the form 2p-13063 – perfect totient number3067 – super-prime3071 – Thabit number3072 – 3-smooth number 3075 – nonagonal number3078 – 18th pentagonal pyramidal number3080 – pronic number3081 – triangular number, 497th sphenic number3087 – sum of first 40 primes

3109 – super-prime3119 – safe prime3121 – centered square number, emirp, largest minimal prime in quinary.3125 – a solution to the expression, where .3136 = 56², palindromic in ternary, tribonacci number3137 – Proth prime, both a left- and right-truncatable prime3149 – highly cototient number3150 = 15³ - 15²3155 – member of the Mian–Chowla sequence3159 = number of trees with 14 unlabeled nodes3160 – triangular number3167 – safe prime3169 – super-prime, Cuban prime of the form.

3203 – safe prime3207 – number of compositions of 14 whose run-lengths are either weakly increasing or weakly decreasing3229 – super-prime3240 – triangular number3248 – 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, centered octagonal number, member of a Ruth–Aaron pair with 3248 under second definition3253 – sum of eleven consecutive primes 3256 – centered heptagonal number3259 – super-prime, completes the ninth prime quadruplet set3264 – solution to Steiner's conic problem: number of smooth conics tangent to 5 given conics in general position3266 – sum of first 41 primes, 523rd sphenic number3276 – tetrahedral number3277 – 5th super-Poulet number, decagonal number3279 – first composite Wieferich number3281 – octahedral number, centered square number3286 – nonagonal number3299 – 85th Sophie Germain prime, super-prime

3306 – pronic number3307 – balanced prime3313 – balanced prime, star number3319 – super-prime, happy number3321 – triangular number3329 – 86th Sophie Germain prime, Proth prime, member of the Padovan sequence3354 – member of the Mian–Chowla sequence3358 – sum of the squares of the first eleven primes3359 – 87th Sophie Germain prime, highly cototient number3360 – largely composite number3363/2378 ≈ √23364 = 58²3367 = 15³ - 2³ = 16³ - 9³ = 34³ - 33³3375 = 15³, palindromic in base 14, 15th cube3389 – 88th Sophie Germain prime

3403 – triangular number3407 – super-prime3413 – 89th Sophie Germain prime, sum of the first 5 nⁿ: 3413 = 1¹ + 2² + 3³ + 4⁴ + 5⁵3422 – pronic number, 553rd sphenic number, melting point of tungsten in degrees Celsius3435 – a perfect digit-to-digit invariant, equal to the sum of its digits to their own powers 3439 – magic constant of n×''n normal magic square and n''-queens problem for n = 19.3445 – centered square number3447 – sum of first 42 primes3449 – 90th Sophie Germain prime3456 – 3-smooth number 3457 – Proth prime3463 – happy number3467 – safe prime3469 – super-prime, Cuban prime of the form x = y + 2, completes the tenth prime quadruplet set3473 – centered heptagonal number3481 = 59², centered octagonal number3486 – triangular number3491 – 91st Sophie Germain prime

3504 – nonagonal number3510 – decagonal number3511 – largest known Wieferich prime3512 – number of primes.3517 – super-prime, sum of nine consecutive primes 3539 – 92nd Sophie Germain prime3540 – pronic number3559 – super-prime3569 – highly cototient number3570 – triangular number3571 – 500th prime, Cuban prime of the form x = y + 1, 17th Lucas number, 4th balanced prime of order 4.3591 – member of the Mian–Chowla sequence3593 – 93rd Sophie Germain prime, super-prime

3600 = 60², number of seconds in an hour, called šār or šāru in the sexagesimal system of Ancient Mesopotamia, 1201-gonal number3601 – star number3610 – 19th pentagonal pyramidal number3613 – centered square number3617 – sum of eleven consecutive primes 3623 – 94th Sophie Germain prime, safe prime3637 – balanced prime, super-prime3638 – sum of first 43 primes, 599th sphenic number3643 – happy number, sum of seven consecutive primes 3654 – tetrahedral number3655 – triangular number, 601st sphenic number3660 – pronic number3684 – 13th Keith number3697 – centered heptagonal number

3721 = 61², centered octagonal number3729 – nonagonal number3733 – balanced prime, super-prime3741 – triangular number, 618th sphenic number3751 – decagonal number3761 – 95th Sophie Germain prime, super-prime3779 – 96th Sophie Germain prime, safe prime3780 – largely composite number3782 – pronic number, 623rd sphenic number3785 – centered square number3797 – member of the Mian–Chowla sequence, both a left- and right- truncatable prime

3803 – 97th Sophie Germain prime, safe prime, the largest prime factor of 123,456,7893821 – 98th Sophie Germain prime3828 – triangular number3831 – sum of first 44 primes3840 = 16³ - 16², double factorial of 10 3844 = 62²3851 – 99th Sophie Germain prime3856 – number of 17-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed3863 – 100th Sophie Germain prime3865 – greater of third pair of Smith brothers3888 – longest number when expressed in Roman numerals I, V, X, L, C, D, and M, 3-smooth number 3889 – Cuban prime of the form x = y + 23894 – octahedral number

3901 – star number3906 – pronic number3911 – 101st Sophie Germain prime, super-prime3914 – number of 18-bead necklaces where complements are equivalent3916 – triangular number3925 – centered cube number3926 – 12th open meandric number, 654th sphenic number3928 – centered heptagonal number3937 – product of distinct Mersenne primes, repeated sum of divisors is prime, denominator of conversion factor from meter to US survey foot3940 – there are 3940 distinct ways to arrange the 12 flat pentacubes into a 3x4x5 box 3943 – super-prime3947 – safe prime3960 – largely composite number3961 – nonagonal number, centered square number3969 = 63², centered octagonal number3989 – highly cototient number3998 – member of the Mian–Chowla sequence3999 – largest number properly expressible using Roman numerals I, V, X, L, C, D, and M, ignoring vinculum

There are 120 prime numbers between 3000 and 4000: