Английская Википедия:100,000

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Шаблон:Redirect Шаблон:Infobox number 100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 10⁵.

Terms for 100,000

In Bangladesh, India, Pakistan and South Asia, one hundred thousand is called a lakh, and is written as 1,00,000. The Thai, Lao, Khmer and Vietnamese languages also have separate words for this number: Шаблон:Lang, Шаблон:Lang, Шаблон:Lang (all saen), and Шаблон:Lang respectively. The Malagasy word is Шаблон:Lang.

In Cyrillic numerals, it is known as the legion (Шаблон:Script): Файл:Legion-1000000-Cyrillic.svg or Файл:Несведь.svg.

Values of 100,000

In astronomy, 100,000 metres, 100 kilometres, or 100 km (62 miles) is the altitude at which the Fédération Aéronautique Internationale (FAI) defines spaceflight to begin.

In the Irish language, Шаблон:Lang (Шаблон:IPA-ga) is a popular greeting meaning "a hundred thousand welcomes".

Selected 6-digit numbers (100,001–999,999)

100,001 to 199,999

• 100,003 = smallest 6-digit prime number
• 100,128 = smallest triangular number with 6 digits and the 447th triangular number
• 100,151 = twin prime with 100,153
• 100,153 = twin prime with 100,151
• 100,255 = Friedman number
• 100,489 = 317², the smallest 6-digit square
• 101,101 = smallest palindromic Carmichael number
• 101,723 = smallest prime number whose square is a pandigital number containing each digit from 0 to 9
• 102,564 = The smallest parasitic number
• 103,049 = little Schroeder number
• 103,680 = highly totient number
• 103,769 = the number of combinatorial types of 5-dimensional parallelohedra
• 103,823 = 47³, the smallest 6-digit cube and nice Friedman number (−1 + 0 + 3×8×2)³
• 104,480 = number of non-isomorphic set-systems of weight 14.
• 104,723 = the 9,999th prime number
• 104,729 = the 10,000th prime number
• 104,869 = the smallest prime number containing every non-prime digit
• 104,976 = 18⁴, 3-smooth number
• 105,071 = number of triangle-free graphs on 11 vertices
• 105,664 = harmonic divisor number
• 109,376 = 1-automorphic number
• 110,880 = highly composite number
• 111,111 = repunit
• 111,777 = smallest natural number requiring 17 syllables in American English, 19 in British English
• 113,634 = Motzkin number for n = 14
• 114,243/80,782 ≈ √2
• 114,689 = prime factor of F₁₂
• 115,975 = Bell number
• 116,281 = 341², square number, centered decagonal number, 18-gonal number
• 117,067 = first vampire prime
• 117,649 = 7⁶
• 117,800 = harmonic divisor number
• 120,032 = number of primitive polynomials of degree 22 over GF(2)
• 120,284 = Keith number
• 120,960 = highly totient number
• 121,393 = Fibonacci number
• 124,000 = number of Islamic prophets
• 125,673 = logarithmic number
• 127,777 = smallest natural number requiring 18 syllables in American English, 20 in British English
• 127,912 = Wedderburn–Etherington number
• 128,981 = Starts the first prime gap sequence of 2, 4, 6, 8, 10, 12, 14
• 129,106 = Keith number
• 130,321 = 19⁴
• 131,071 = Mersenne prime
• 131,072 = 2¹⁷
• 131,361 = Leyland number
• 134,340 = Pluto's minor planet designation
• 135,137 = Markov number
• 142,129 = 377², square number, dodecagonal number
• 142,857 = Kaprekar number, smallest cyclic number in decimal.
• 144,000 = number with religious significance
• 147,640 = Keith number
• 148,149 = Kaprekar number
• 152,381 = unique prime in base 20
• 156,146 = Keith number
• 160,000 = 20⁴
• 160,176 = number of reduced trees with 26 nodes
• 161,051 = 11⁵
• 161,280 = highly totient number
• 166,320 = highly composite number
• 167,400 = harmonic divisor number
• 167,894 = number of ways to partition {1,2,3,4,5,6,7,8} and then partition each cell (block) into subcells.
• 173,600 = harmonic divisor number
• 174,680 = Keith number
• 174,763 = Wagstaff prime
• 176,906 = number of 24-bead necklaces (turning over is allowed) where complements are equivalent
• 177,147 = 3¹¹
• 177,777 = smallest natural number requiring 19 syllables in American English, 21 in British English
• 178,478 = Leyland number
• 181,440 = highly totient number
• 181,819 = Kaprekar number
• 182,362 = number of 23-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 183,186 = Keith number
• 183,231 = number of partially ordered set with 9 unlabeled elements
• 187,110 = Kaprekar number
• 194,481 = 21⁴
• 195,025 = Pell number, Markov number
• 196,418 = Fibonacci number, Markov number
• 196,560 = the kissing number in 24 dimensions
• 196,883 = the dimension of the smallest nontrivial irreducible representation of the Monster group
• 196,884 = the coefficient of q in the Fourier series expansion of the j-invariant. The adjacency of 196883 and 196884 was important in suggesting monstrous moonshine.
• 199,999 = prime number.

200,000 to 299,999

• 202,717 = k such that the sum of the squares of the first k primes is divisible by k.
• 206,098 – Large Schröder number
• 206,265 = rounded number of arc seconds in a radian (see also parsec), since Шаблон:Sfrac = 206,264.806...
• 207,360 = highly totient number
• 208,012 = the Catalan number C₁₂
• 208,335 = the largest number to be both triangular and square pyramidal
• 208,495 = Kaprekar number
• 212,159 = smallest unprimeable number ending in 1, 3, 7 or 9
• 221,760 = highly composite number
• 222,222 = repdigit
• 227,475 = Riordan number
• 234,256 = 22⁴
• 237,510 = harmonic divisor number
• 238,591 = number of free 13-ominoes
• 241,920 = highly totient number
• 242,060 = harmonic divisor number
• 248,832 = 12⁵, 100,000₁₂, AKA a gross-great-gross (100₁₂ great-grosses); the smallest fifth power that can be represented as the sum of only 6 fifth powers: 12⁵ = 4⁵ + 5⁵ + 6⁵ + 7⁵ + 9⁵ + 11⁵
• 262,144 = 2¹⁸; exponential factorial of 4; a superperfect number
• 262,468 = Leyland number
• 268,705 = Leyland number
• 274,177 = prime factor of the Fermat number F₆
• 275,807/195,025 ≈ √2
• 276,480 = number of primitive polynomials of degree 24 over GF(2)
• 277,200 = highly composite number
• 279,841 = 23⁴
• 279,936 = 6⁷
• 280,859 = a prime number whose square 78881777881 is tridigital
• 291,400 = number of non-equivalent ways of expressing 100,000,000 as the sum of two prime numbers
• 293,547 = Wedderburn–Etherington number
• 294,001 = smallest weakly prime number in base 10
• 294,685 = Markov number
• 298,320 = Keith number

300,000 to 399,999

• 310,572 = Motzkin number
• 316,749 = number of reduced trees with 27 nodes
• 317,811 = Fibonacci number
• 318,682 = Kaprekar number
• 325,878 = Fine number
• 326,981 = alternating factorial
• 329,967 = Kaprekar number
• 331,776 = 24⁴
• 332,640 = highly composite number; harmonic divisor number
• 333,333 = repdigit
• 333,667 = sexy prime and unique prime
• 333,673 = sexy prime with 333,679
• 333,679 = sexy prime with 333,673
• 337,500 = 2² × 3³ × 5⁵
• 337,594 = number of 25-bead necklaces (turning over is allowed) where complements are equivalent
• 349,716 = number of 24-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 351,351 = only known odd abundant number that is not the sum of some of its proper, nontrivial (i.e. >1) divisors Шаблон:OEIS.
• 351,352 = Kaprekar number
• 355,419 = Keith number
• 356,643 = Kaprekar number
• 356,960 = number of primitive polynomials of degree 23 over GF(2)
• 360,360 = harmonic divisor number; the smallest number divisible by all of the numbers 1 through 15
• 362,880 = 9!, highly totient number
• 369,119 = prime number which divides the sum of all primes less than or equal to it
• 370,261 = first prime followed by a prime gap of over 100
• 371,293 = 13⁵, palindromic in base 12 (15AA51₁₂)
• 389,305 = self-descriptive number in base 7
• 390,313 = Kaprekar number
• 390,625 = 5⁸
• 397,585 = Leyland number

400,000 to 499,999

• 409,113 = sum of the first nine factorials
• 422,481 = smallest number whose fourth power is the sum of three smaller fourth powers
• 423,393 = Leyland number
• 426,389 = Markov number
• 426,569 = cyclic number in base 12
• 437,760 to 440,319 = Шаблон:Anchorany of these numbers will cause the Apple II+ and Apple IIe computers to crash to a monitor prompt when entered at the BASIC prompt, due to a short-cut in the Applesoft code programming of the overflow test when evaluating 16-bit numbers. Entering 440000 at the prompt has been used to hack games that are protected against entering commands at the prompt after the game is loaded.
• 444,444 = repdigit
• 456,976 = 26⁴
• 461,539 = Kaprekar number
• 466,830 = Kaprekar number
• 470,832 = Pell number
• 483,840 = highly totient number
• 498,960 = highly composite number
• 499,393 = Markov number
• 499,500 = Kaprekar number

500,000 to 599,999

• 500,500 = Kaprekar number, sum of first 1,000 integers
• 509,203 = Riesel number
• 510,510 = the product of the first seven prime numbers, thus the seventh primorial. It is also the product of four consecutive Fibonacci numbers—13, 21, 34, 55, the highest such sequence of any length to be also a primorial. And it is a double triangular number, the sum of all even numbers from 0 to 1428.
• 514,229 = Fibonacci prime, Markov prime
• 518,859 = little Schroeder number
• 524,287 = Mersenne prime
• 524,288 = 2¹⁹
• 524,649 = Leyland number
• 525,600 = minutes in a non-leap year
• 527,040 = minutes in a leap year
• 531,441 = 3¹²
• 533,169 = Leyland number
• 533,170 = Kaprekar number
• 537,824 = 14⁵
• 539,400 = harmonic divisor number
• 548,834 = equal to the sum of the sixth powers of its digits
• 554,400 = highly composite number
• 555,555 = repdigit
• 599,999 = prime number.

600,000 to 699,999

• 604,800 = number of seconds in a week
• 614,656 = 28⁴
• 625,992 = Riordan number
• 629,933 = number of reduced trees with 28 nodes
• 646,018 = Markov number
• 649,532 = number of 26-bead necklaces (turning over is allowed) where complements are equivalent
• 664,579 = the number of primes under 10,000,000
• 665,280 = highly composite number
• 665,857/470,832 ≈ √2
• 666,666 = repdigit
• 671,092 = number of 25-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 676,157 = Wedderburn–Etherington number
• 678,570 = Bell number
• 694,280 = Keith number
• 695,520 = harmonic divisor number

700,000 to 799,999

• 700,001 = prime number.
• 707,281 = 29⁴
• 720,720 = superior highly composite number; colossally abundant number; the smallest number divisible by all the numbers 1 through 16
• 725,760 = highly totient number
• 726,180 = harmonic divisor number
• 729,000 = 90³
• 739,397 = largest prime that is both right- and left-truncatable.
• 742,900 = Catalan number
• 753,480 = harmonic divisor number
• 759,375 = 15⁵
• 765,623 = emirp, Friedman prime 5⁶ × 7² − 6 ÷ 3
• 777,777 = repdigit, smallest natural number requiring 20 syllables in American English, 22 in British English, largest number in English not containing the letter 'i' in its name
• 783,700 = initial number of third century xx00 to xx99 (after 400 and 1,400) containing seventeen prime numbersШаблон:Efn {783,701, 783,703, 783,707, 783,719, 783,721, 783,733, 783,737, 783,743, 783,749, 783,763, 783,767, 783,779, 783,781, 783,787, 783,791, 783,793, 783,799}
• 799,999 = prime number.

800,000 to 899,999

• 810,000 = 30⁴
• 823,543 = 7⁷
• 825,265 = smallest Carmichael number with 5 prime factors
• 832,040 = Fibonacci number
• 853,467 = Motzkin number
• 857,375 = 95³
• 873,612 = 1¹ + 2² + 3³ + 4⁴ + 5⁵ + 6⁶ + 7⁷
• 888,888 = repdigit
• 890,625 = 1-automorphic number

900,000 to 999,999

• 900,001 = prime number
• 901,971 = number of free 14-ominoes
• 909,091 = unique prime in base 10
• 923,521 = 31⁴
• 925,765 = Markov number
• 925,993 = Keith number
• 950,976 = harmonic divisor number
• 967,680 = highly totient number
• 970,299 = 99³, the largest 6-digit cube
• 998,001 = 999², the largest 6-digit square. The reciprocal of this number, in its expanded form, lists all three-digit numbers in order except 998.
• 998,991 = largest triangular number with 6 digits and the 1413th triangular number
• 999,983 = largest 6-digit prime number
• 999,999 = repdigit. Rational numbers with denominators 7 and 13 have 6-digit repetends when expressed in decimal form, because 999999 is the smallest number one less than a power of 10 that is divisible by 7 and by 13, and it is the largest number in English not containing the letter 'l' in its name.

Prime numbers

There are 9,592 primes less than 10⁵, where 99,991 is the largest prime number smaller than 100,000.

Increments of 10⁵ from 100,000 through a one million have the following prime counts:

• 8,392 primes between 100,000 and 200,000.Шаблон:Efn

This is a difference of 1,200 primes from the previous range.

104,729 is the 10,000th prime in this range.

199,999 is prime.

• 8,013 primes between 200,000 and 300,000.Шаблон:Efn

A difference of 379 primes from the previous range.

224,737 is the 20,000th prime.

• 7,863 primes between 300,000 and 400,000.Шаблон:Efn

A difference of 150 primes from the previous range.

350,377 is the 30,000th prime.

• 7,678 primes between 400,000 and 500,000.Шаблон:Efn

A difference of 185 primes from the previous range.

Here, the difference increases by a count of 35.

479,909 is the 40,000th prime.

• 7,560 primes between 500,000 and 600,000.Шаблон:Efn

A difference of 118 primes from the previous range.

7,560 is the twentieth highly composite number.

599,999 is prime.

• 7,445 primes between 600,000 and 700,000.Шаблон:Efn

A difference of 115 primes from the previous range.

611,953 is the 50,000th prime.

• 7,408 primes between 700,000 and 800,000.Шаблон:Efn

A difference of 37 primes from the previous range.

700,001 and 799,999 are both prime.

746,773 is the 60,000th prime.

• 7,323 primes between 800,000 and 900,000.Шаблон:Efn

A difference of 85 primes from the previous range.

Here, the difference increases by a count of 48.

882,377 is the 70,000th prime.

• 7,224 primes between 900,000 and 1,000,000.Шаблон:Efn

A difference of 99 primes from the previous range.

The difference increases again, by a count of 14.

900,001 is prime.

In total, there are 68,906 prime numbers between 100,000 and 1,000,000.