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, dodecagonal number

3037 – star number, cousin prime with 3041

3046 – centered heptagonal number

3052 – decagonal number

3059 – centered cube number

3063 – perfect totient number

3067 – super-prime

3071 – Thabit number

3075 – nonagonal number

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, emirp, largest minimal prime in quinary.

3136 = 562, palindromic in ternary (110220113), tribonacci number

3137 – Proth prime, both a left- and right-truncatable prime

3149 – highly cototient number

3155 – member of the Mian–Chowla sequence

3159 = number of trees with 14 unlabeled nodes

3160 – triangular number

3167 – safe prime

3169 – super-prime, Cuban prime of the form

x

=

y

+

1

{\displaystyle x=y+1}

.

3192 – pronic number

3200 to 3299

3203 – safe prime

3229 – super-prime

3240 – triangular number

3248 – member of a Ruth-Aaron pair with 3249 under second definition

3249 = 572, palindromic in base 7 (123217), centered octagonal number, member of a Ruth–Aaron pair with 3248 under second definition

3256 – centered heptagonal number

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

3266 – sum of first 41 primes, 523rd sphenic number

3276 – tetrahedral number

3277 – 5th super-Poulet number, decagonal number

3279 – first composite Wieferich number

3281 – octahedral number, centered square number

3286 – nonagonal number

3299 – 85th Sophie Germain prime, super-prime

3300 to 3399

3306 – pronic number

3307 – balanced prime

3313 – balanced prime, star number

3319 – super-prime, happy number

3321 – triangular number

3329 – 86th Sophie Germain prime, Proth prime, member of the Padovan sequence

3354 – member of the Mian–Chowla sequence

3359 – 87th Sophie Germain prime, highly cototient number

3360 – largely composite number

3389 – 88th Sophie Germain prime

3400 to 3499

3403 – triangular number

3407 – super-prime

3413 – 89th Sophie Germain prime

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

3447 – sum of first 42 primes

3449 – 90th Sophie Germain prime

3457 – Proth prime

3463 – happy number

3467 – safe prime

3469 – super-prime, Cuban prime of the form x = y + 2, completes the tenth prime quadruplet set

3473 – centered heptagonal number

3481 = 592, centered octagonal number

3486 – triangular number

3491 – 91st Sophie Germain prime

3500 to 3599

3504 – nonagonal number

3510 – decagonal number

3511 – largest known Wieferich prime

3512 – number of primes

≤

2

15

{\displaystyle \leq 2^{15}}

.

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

3570 – triangular number

3571 – 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 sequence

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.