100,000 Explained

Number:	100000
Lang1:	Egyptian hieroglyph
Lang1 Symbol:

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: Thai: แสน, Lao: ແສນ, Central Khmer: សែន (all saen), and Vietnamese: ức respectively. The Malagasy word is Malagasy: hetsy.^[1]

In the Netherlands, a 'ton' is a colloquialism for a denomination of 100.000 monetary units. In the guilders period a ton would denote 100.000 guilders. With the introduction of the euro, a ton would come to mean 100.000 euros. The usage is mostly limited to the financial sphere and the buying and selling of houses. It is not used in official settings because of the ambiguity with commonly used metric tonne. While usage is common in the Netherlands, it sees almost no use in Belgium.

In Cyrillic numerals, it is known as the legion : or .

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 paleoclimatology, the 100,000-year problem is a mismatch between the temperature record and the modeled incoming solar radiation.

In the Irish language, Irish: céad míle [[fáilte]] (in Irish pronounced as /ˌceːd̪ˠ ˈmʲiːlʲə ˈfˠaːl̠ʲtʲə/) 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^[2]
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 = Schröder–Hipparchus 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
105,558 = number of partitions of 46
105,664 = harmonic divisor number
108,968 = number of signed trees with 11 nodes
109,376 = 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
123,717 = smallest digitally balanced number in base 7^[3]
123,867 = number of trees with 18 unlabeled nodes
124,754 = number of partitions of 47
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 and largest determinant of a (real) -matrix of order 15.^[4]
131,361 = Leyland number
134,340 = Pluto's minor planet designation
135,135 = double factorial of 13
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
147,273 = number of partitions of 48
147,640 = Keith number
148,149 = Kaprekar number
152,381 = unique prime in base 20
156,146 = Keith number
155,921 = smallest prime number being the only prime in an interval from 100n to 100n + 99
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 and then partition each cell (block) into subcells.
173,525 = number of partitions of 49
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
189,819 = number of letters in the longest English word, taking 3 hours to pronounce^[5]
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 = 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^[6]
208,495 = Kaprekar number
212,159 = smallest unprimeable number ending in 1, 3, 7 or 9^[7]
221,760 = highly composite number
222,222 = repdigit
224,737 = the 20,000th prime number
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
253,293 = number of prime knots with 15 crossings
255,168 = number of ways to play tic tac toe^[8]
262,144 = 2¹⁸; exponential factorial of 4;^[9] 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^[10]
294,685 = Markov number
298,320 = Keith number

300,000 to 399,999

310,572 = Motzkin number
314,159 = pi-prime
316,749 = number of reduced trees with 27 nodes
317,811 = Fibonacci number
317,955 = number of trees with 19 unlabeled nodes
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 .
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; smallest number divisible by the numbers from 1 to 15 (there is no smaller number divisible by the numbers from 1 to 14 since any number divisible by 3 and 5 must be divisible by 15)
362,880 = 9!, highly totient number
369,119 = prime number which divides the sum of all primes less than or equal to it^[11]
369,293 = smallest prime with the property that inserting a digit anywhere in the number will always yield a composite^[12]
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 = any 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.^[13] 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
492,638 = number of signed trees with 12 nodes
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 largest 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,
518,859 = Schröder–Hipparchus 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
586,081 = number of prime numbers having seven digits.
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
645,120 = double factorial of 14
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; smallest number divisible by the numbers from 1 to 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 numbers
799,999 = prime number.

800,000 to 899,999

810,000 = 30⁴
823,065 = number of trees with 20 unlabeled nodes
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 = 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
956,619: 956619^2=915119911161, and only the digits 1, 5, 6 and 9 are used in both this number and its square.
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.^[14]
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. 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. 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. 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. 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. 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. 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. 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. 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. 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.^[15]

Notes and References

Web site: Malagasy Dictionary and Madagascar Encyclopedia : hetsy. 26 October 2017. malagasyword.org. 2019-12-31.
Web site: Problem of the Month (August 2000) . 2013-01-13 . live . https://web.archive.org/web/20121218102647/http://www2.stetson.edu/~efriedma/mathmagic/0800.html . 2012-12-18 .
a(1) = 1; for n > 1, smallest digitally balanced number in base n.
2024-03-30 .
Web site: The longest word in English? Here are the top 15 biggest ones . 2024-03-01 . Berlitz . en.
Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.
Book: Collins, Julia. Numbers in Minutes. Quercus. 2019. 978-1635061772. United Kingdom. 140.
Web site: How many Tic-Tac-Toe (Noughts and crosses) games? .
a(0)=1, a(n+1) = (n+1)^a(n).
Web site: Weißstein. Eric W.. 25 December 2020. Weakly Prime. Wolfram MathWorld.
Primes p with property that p divides the sum of all primes <= p.
Non-insertable primes: primes with property that no matter where you insert (or prepend or append) a digit you get a composite number (except for prepending a zero)..
Web site: Applesoft Disassembly -- S.d912 . 2016-04-04 . live . https://web.archive.org/web/20160415032535/http://www.txbobsc.com/scsc/scdocumentor/D912.html . 2016-04-15 . Disassembled ROM. See comments at $DA1E.
Web site: Dividing one by 998001 produces list of three digit numbers . 23 January 2012 .
Web site: The Nth Prime Page . Caldwell . Chris K. . PrimePages . PrimePages . 2022-12-03 . From the differences of the prime indexes of the smallest and largest prime numbers in ranges of increments of 10⁵, plus 1 (for each range).