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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). 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 number *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 *3045 – sum of the integers 196 to 210 and sum of the integers 211 to 224 *3046 – centered heptagonal number *3052 – decagonal number *3059 – centered cube number *3061 – prime of the form 2p-1 *3063 – perfect totient number *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 *3078 – 18th pentagonal pyramidal 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 *3125 – 55 *3136 – 562, palindromic in base 3 (110220113), tribonacci number *3137 – Proth prime, both a left- and right- truncatable prime *3149 – highly cototient number *3155 – member of the Mian–Chowla sequence *3160 – triangular number *3167 – safe prime *3169 – super-prime, Cuban prime of the form 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, 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, 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 *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 *3281 – octahedral number, centered square number *3286 – nonagonal number *3299 – 85th Sophie Germain prime, super-prime 3300 to 3399 *3301 – a normal prime number *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 *3358 – sum of the squares of the first eleven primes *3359 – 87th Sophie Germain prime, highly cototient number *3364 – 582 *3367 – 153 \- 23 = 163 \- 93 = 343 \- 333 *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 *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 *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. Saros), 1201-gonal number *3601 – star number *3610 – 19th pentagonal pyramidal number *3613 – centered square number *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 *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 *3655 – triangular number, 601st sphenic number *3660 – pronic number *3684 – 13th Keith number *3697 – centered heptagonal number 3700 to 3799 *3721 – 612, centered octagonal number *3729 – nonagonal number *3733 – balanced prime, super-prime *3741 – triangular number, 618th sphenic number *3751 – decagonal number *3761 – 95th Sophie Germain prime, super-prime *3779 – 96th Sophie Germain prime, safe prime *3782 – pronic number, 623rd sphenic number *3785 – centered square number *3797 – member of the Mian–Chowla sequence, 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 *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 *3894 – octahedral number 3900 to 3999 *3901 – star number *3906 – pronic number *3911 – 101st Sophie Germain prime, super-prime *3916 – triangular number *3925 – centered cube number *3926 – 12th open meandric number, 654th sphenic number *3928 – centered heptagonal number *3937 – product of distinct Mersenne primes, repeated sum of divisors is prime, denominator of conversion factor from meter to US survey foot *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, centered square number *3967 – Carol number *3969 – 632, centered octagonal number *3989 – highly cototient number *3998 – member of the Mian–Chowla sequence *3999 – largest number properly expressible using Roman numerals I, V, X, L, C, D, and M (MMMCMXCIX), ignoring vinculum References Category:Integers "
"4000 (four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number. Selected numbers in the range 4001–4999 4001 to 4099 * 4005 – triangular number * 4007 – safe prime * 4010 – magic constant of n × n normal magic square and n-queens problem for n = 20. * 4013 – balanced prime * 4019 – Sophie Germain prime * 4027 – super-prime * 4028 – sum of the first 45 primes * 4030 – third weird number * 4031 – sum of the cubes of the first six primes * 4032 – pronic number * 4033 – sixth super- Poulet number; strong pseudoprime in base 2 * 4060 – tetrahedral number * 4073 – Sophie Germain prime * 4079 – safe prime * 4091 – super-prime * 4092 – an occasional glitch in the game The Legend of Zelda: Ocarina of Time causes the Gossip Stones to say this number * 4095 – triangular number, odd abundant number, * 4096 – power of two 212; 642; 16th cube; smallest number with exactly 13 divisors; a superperfect number 4100 to 4199 * 4104 – 23 \+ 163 = 93 \+ 153 (taxicab number) * 4127 – safe prime * 4133 – super-prime * 4139 – safe prime * 4140 – Bell number * 4141 – centered square number * 4147 – smallest cyclic number in duodecimal * 4153 – super-prime * 4160 – pronic number * 4166 – centered heptagonal number, * 4167 – 7! − 6! − 5! − 4! − 3! − 2! − 1! * 4177 – prime of the form 2p-1 * 4181 – Fibonacci number, Markov number * 4186 – triangular number * 4187 – factor of R13. Also record number of wickets taken in first-class cricket by Wilfred Rhodes. * 4199 – highly cototient number, product of three consecutive primes 4200 to 4299 * 4200 – nonagonal number, pentagonal pyramidal number, * 4210 – 11th semi- meandric number * 4211 – Sophie Germain prime * 4217 – super-prime, happy number * 4219 – cuban prime of the form x = y + 1, centered hexagonal number * 4223 – Kynea number * 4225 – 652, centered octagonal number * 4227 – sum of the first 46 primes * 4240 – Leyland number * 4257 – decagonal number * 4259 – safe prime * 4261 – prime of the form 2p-1 * 4271 – Sophie Germain prime * 4273 – super-prime * 4278 – triangular number * 4283 – safe prime * 4289 – highly cototient number * 4290 – pronic number 4300 to 4399 * 4324 – 23rd square pyramidal number * 4325 – centered square number * 4339 – super- prime, twin prime * 4349 – Sophie Germain prime * 4356 – 662, sum of the cubes of the first eleven integers * 4357 – prime of the form 2p-1 * 4359 – perfect totient number * 4369 – seventh super-Poulet number * 4371 – triangular number * 4373 – Sophie Germain prime * 4375 – perfect totient number (the smallest not divisible by 3) * 4391 – Sophie Germain prime * 4397 – Year of Comet Hale–Bopp's return, super-prime 4400 to 4499 * 4400 – the number of missing persons in the sci-fi show The 4400 * 4409 – Sophie Germain prime, highly cototient number, balanced prime, 600th prime number * 4410 – member of the Padovan sequence * 4411 – centered heptagonal number * 4421 – super-prime, alternating factorial * 4422 – pronic number * 4438 – sum of the first 47 primes * 4446 – nonagonal number * 4447 – cuban prime of the form x = y + 1 * 4457 – balanced prime * 4463 – super-prime * 4465 – triangular number * 4481 – Sophie Germain prime * 4489 – 672, centered octagonal number * 4495 – tetrahedral number 4500 to 4599 * 4503 – largest number not the sum of four or fewer squares of composites * 4505 – fifth Zeisel number * 4513 – centered square number * 4516 – centered pentagonal number * 4517 – super- prime, happy number * 4522 – decagonal number * 4547 – safe prime * 4549 – super-prime * 4556 – pronic number * 4560 – triangular number * 4567 – super- prime * 4579 – octahedral number * 4597 – balanced prime 4600 to 4699 * 4607 – Woodall number * 4619 – highly cototient number * 4621 – prime of the form 2p-1 * 4624 – 682 * 4641 – magic constant of n × n normal magic square and n-queens problem for n = 21. * 4656 – triangular number * 4657 – balanced prime * 4661 – sum of the first 48 primes * 4663 – super-prime, centered heptagonal number * 4679 – safe prime * 4681 – eighth super-Poulet number * 4691 – balanced prime * 4692 – pronic number * 4699 – nonagonal number 4700 to 4799 * 4703 – safe prime * 4705 – 482 \+ 492 = 172 \+ 182 \+ … + 262, centered square number * 4727 – sum of the squares of the first twelve primes * 4731 – centered pentagonal number * 4733 – Sophie Germain prime * 4753 – triangular number * 4759 – super-prime * 4761 – 692, centered octagonal number * 4787 – safe prime, super-prime * 4788 – 14th Keith number * 4793 – Sophie Germain prime * 4795 – decagonal number * 4799 – safe prime 4800 to 4899 * 4801 – super-prime, cuban prime of the form x = y + 2, smallest prime with a composite sum of digits in base 7 * 4830 – pronic number * 4851 – triangular number, pentagonal pyramidal number * 4862 – Catalan number * 4871 – Sophie Germain prime * 4877 – super-prime * 4879 – 11th Kaprekar number * 4888 – sum of the first 49 primes 4900 to 4999 * 4900 – 702, the only square- pyramidal square other than 1 * 4901 – centered square number * 4913 – 17th cube * 4919 – Sophie Germain prime, safe prime * 4922 – centered heptagonal number * 4933 – super-prime * 4941 – centered cube number * 4943 – Sophie Germain prime, super-prime * 4950 – triangular number, 12th Kaprekar number * 4951 – centered pentagonal number * 4957 – sum of three and five consecutive primes (1637 + 1657 + 1663, 977 + 983 + 991 + 997 + 1009) * 4959 – nonagonal number * 4960 – tetrahedral number; greater of fourth pair of Smith brothers * 4970 – pronic number * 4991 – Lucas–Carmichael number * 4993 – balanced prime References Category:Integers "
"5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic number in the English language. Selected numbers in the range 5001–5999 5001 to 5099 * 5003 – Sophie Germain prime * 5020 – amicable number with 5564 * 5021 – super-prime, twin prime * 5039 – factorial prime, Sophie Germain prime * 5040 – 7!, superior highly composite number * 5041 – 712, centered octagonal number * 5050 – triangular number, Kaprekar number, sum of first 100 integers * 5051 – Sophie Germain prime * 5059 – super-prime * 5076 – decagonal number * 5081 – Sophie Germain prime * 5087 – safe prime * 5099 – safe prime 5100 to 5199 * 5107 – super-prime, balanced prime * 5113 – balanced prime * 5117 - sum of the first 50 primes * 5151 – triangular number * 5167 – cuban prime of the form x = y + 1 * 5171 – Sophie Germain prime * 5184 – 722 * 5186 – φ(5186) = 2592 * 5187 – φ(5187) = 2592 * 5188 – φ(5189) = 2592, centered heptagonal number * 5189 – super-prime 5200 to 5299 * 5226 – nonagonal number * 5231 – Sophie Germain prime * 5244 – 222 \+ 232 \+ … + 292 = 202 \+ 212 \+ … + 282 * 5249 – highly cototient number * 5253 – triangular number * 5279 – Sophie Germain prime, 700th prime number * 5280 is the number of feet in a mile. It is divisible by three, yielding exactly 1760 yards per mile and by 16.5, yielding exactly 320 rods per mile. * 5280 is connected with both Klein's J-invariant and the Heegner numbers. Specifically : 5280 = -\sqrt[3]{j\left( {\scriptstyle\frac{1}{2}} \left( 1 + i\sqrt{67}\, \right)\right) }. * 5281 – super-prime, twin prime * 5292 – Kaprekar number 5300 to 5399 * 5303 – Sophie Germain prime, balanced prime * 5329 – 732, centered octagonal number * 5333 – Sophie Germain prime * 5335 – magic constant of n × n normal magic square and n-queens problem for n = 22. * 5340 – octahedral number * 5356 – triangular number * 5365 – decagonal number * 5381 – super-prime * 5387 – safe prime, balanced prime * 5392 – Leyland number * 5393 – balanced prime * 5399 – Sophie Germain prime, safe prime 5400 to 5499 * 5405 – member of a Ruth–Aaron pair with 5406 (either definition) * 5406 – member of a Ruth–Aaron pair with 5405 (either definition) * 5419 – Cuban prime of the form x = y + 1 * 5441 – Sophie Germain prime, super-prime * 5456 – tetrahedral number * 5459 – highly cototient number * 5460 – triangular number * 5461 – super-Poulet number, centered heptagonal number * 5476 – 742 * 5483 – safe prime 5500 to 5599 * 5500 – nonagonal number * 5501 – Sophie Germain prime * 5503 – super-prime, twin prime with 5501, cousin prime with 5507 * 5507 – safe prime * 5525 – square pyramidal number * 5527 – happy number * 5536 – tetranacci number * 5557 – super prime * 5563 – balanced prime * 5564 – amicable number with 5020 * 5565 – triangular number * 5566 – pentagonal pyramidal number * 5569 – happy number * 5571 – perfect totient number * 5581 – prime of the form 2p-1 5600 to 5699 * 5623 – super-prime * 5625 – 752, centered octagonal number * 5639 – Sophie Germain prime, safe prime * 5651 – super-prime * 5659 – happy number, completes the eleventh prime quadruplet set * 5662 – decagonal number * 5671 – triangular number 5700 to 5799 * 5701 – super-prime * 5711 – Sophie Germain prime * 5719 – Zeisel number, Lucas–Carmichael number * 5741 – Sophie Germain prime, Pell number, Markov number, centered heptagonal number * 5749 – super-prime * 5768 – tribonacci number * 5776 – 762 * 5777 – smallest counterexample to the conjecture that all odd numbers are of the form p + 2a2 * 5778 – triangular number * 5781 – nonagonal number * 5798 – Motzkin number 5800 to 5899 * 5801 – super-prime * 5807 – safe prime, balanced prime * 5832 – 183 * 5842 – member of the Padovan sequence * 5849 – Sophie Germain prime * 5869 – super-prime * 5879 – safe prime, highly cototient number * 5886 – triangular number 5900 to 5999 * 5903 – Sophie Germain prime * 5913 – sum of the first seven factorials * 5927 – safe prime * 5929 – 772, centered octagonal number * 5939 – safe prime * 5967 – decagonal number * 5984 – tetrahedral number * 5995 – triangular number References Category:Integers "