100,000 (one hundred thousand) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
following
99,999 and preceding 100,001. In
scientific notation
Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...
, it is written as 10
5.
Terms for 100,000
In
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
,
Pakistan
Pakistan ( ur, ), officially the Islamic Republic of Pakistan ( ur, , label=none), is a country in South Asia. It is the world's fifth-most populous country, with a population of almost 243 million people, and has the world's second-lar ...
and
South Asia
South Asia is the southern subregion of Asia, which is defined in both geographical
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth descr ...
, one hundred thousand is called a
lakh, and is written as 1,00,000. The
Thai,
Lao,
Khmer and
Vietnamese
Vietnamese may refer to:
* Something of, from, or related to Vietnam, a country in Southeast Asia
** A citizen of Vietnam. See Demographics of Vietnam.
* Vietnamese people, or Kinh people, a Southeast Asian ethnic group native to Vietnam
** Overse ...
languages also have separate words for this number: , , (all ''saen''), and respectively. The
Malagasy word is .
In
Cyrillic numerals, it is known as the legion ():
![Legion-1000000-Cyrillic](https://upload.wikimedia.org/wikipedia/commons/d/dc/Legion-1000000-Cyrillic.jpg)
or
![Несведь](https://upload.wikimedia.org/wikipedia/commons/9/9a/%D0%9D%D0%B5%D1%81%D0%B2%D0%B5%D0%B4%D1%8C.jpg)
.
Values of 100,000
In
astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
, 100,000 metres, 100 kilometres, or 100 km (62 miles) is the
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
at which the
Fédération Aéronautique Internationale (FAI) defines
spaceflight
Spaceflight (or space flight) is an application of astronautics to fly spacecraft into or through outer space, either with or without humans on board. Most spaceflight is uncrewed and conducted mainly with spacecraft such as satellites in o ...
to begin.
In the
Irish language
Irish ( Standard Irish: ), also known as Gaelic, is a Goidelic language of the Insular Celtic branch of the Celtic language family, which is a part of the Indo-European language family. Irish is indigenous to the island of Ireland and was ...
, () is a popular greeting meaning "a hundred thousand welcomes".
Selected 6-digit numbers (100,001–999,999)
100,001 to 199,999
100,001 to 199,999
* 100,003 = smallest 6-digit prime number
* 100,128 = smallest
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
with 6 digits and the 447th triangular number
* 100,151 =
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
with 100,153
* 100,153 = twin prime with 100,151
* 100,255 =
Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, pa ...
* 101,101 = smallest
palindromic
A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words ''madam'' or ''racecar'', the date and time ''11/11/11 11:11,'' and the sentence: "A man, a plan, a canal – Pana ...
Carmichael number
In number theory, a Carmichael number is a composite number n, which in modular arithmetic satisfies the congruence relation:
:b^n\equiv b\pmod
for all integers b. The relation may also be expressed in the form:
:b^\equiv 1\pmod.
for all integers ...
* 101,723 = smallest
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
whose square is a
pandigital number
In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 (one billion two hundred thirty four million five hundred sixty seven tho ...
containing each digit from 0 to 9
* 102,564 = The smallest
parasitic number An ''n''-parasitic number (in base 10) is a positive natural number which, when multiplied by ''n'', results in movement of the last digit of its decimal representation to its front. Here ''n'' is itself a single-digit positive natural number. In ...
* 103,049 =
little Schroeder number
* 103,680 =
highly totient number
* 103,769 = the number of combinatorial types of 5-dimensional
parallelohedra
* 103,823 = 47
3, 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
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
containing every non-prime digit
* 104,976 = 18
4, 3-smooth number
* 105,071 = number of triangle-free graphs on 11 vertices
* 105,664 =
harmonic divisor number
In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are:
: 1, 6, 2 ...
* 109,376 = 1-
automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square "ends" in the same digits as the number itself.
Definition and properties
Given a number base b, a natura ...
* 110,880 =
highly composite number
__FORCETOC__
A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...
* 111,111 =
repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book ''Recreat ...
* 111,777 = smallest natural number requiring 17 syllables in American English, 19 in British English
* 113,634 =
Motzkin number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have d ...
for ''n'' = 14
* 114,243/80,782 ≈
√2
* 114,689 =
prime factor of ''
F''
12
* 115,975 =
Bell number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy ...
* 116,281 = 341
2,
square number
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as .
The usu ...
,
centered decagonal number
A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. The centered decagonal number for ''n'' is given by th ...
, 18-gonal number
* 117,067 = first
vampire prime
* 117,649 = 7
6
* 117,800 = harmonic divisor number
* 120,284 =
Keith number
In number theory, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n in a given number base b with k digits such that when a sequence is created such that the first k terms are the k digits of n and ...
* 120,960 = highly totient number
* 121,393 =
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
* 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 The Wedderburn–Etherington numbers are an integer sequence named for Ivor Malcolm Haddon Etherington.. and Joseph Wedderburn. that can be used to count certain kinds of binary trees. The first few numbers in the sequence are
:0, 1, 1, 1, 2, 3, 6, ...
* 128,981 = Starts the first
prime gap
A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g'n'' or ''g''(''p'n'') is the difference between the (''n'' + 1)-th and the
''n''-th prime numbers, i.e.
:g_n = p_ - p_n.\
W ...
sequence of 2, 4, 6, 8, 10, 12, 14
* 129,106 = Keith number
* 130,321 = 19
4
* 131,071 =
Mersenne prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th ...
* 131,072 = 2
17
* 131,361 =
Leyland number In number theory, a Leyland number is a number of the form
:x^y + y^x
where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are
: 8, 17, 32, 54, 57, 100, 145, 177, ...
* 134,340 =
Pluto
Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Sun. It is the largest ...
's minor planet designation
* 135,137 =
Markov number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation
:x^2 + y^2 + z^2 = 3xyz,\,
studied by .
The first few Markov numbers are
: 1, 2, 5, 13, 29, 34, 89 ...
* 142,129 = 377
2,
square number
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as .
The usu ...
,
dodecagonal number
A dodecagonal number is a figurate number that represents a dodecagon. The dodecagonal number for ''n'' is given by the formula
:D_=5n^2 - 4n
The first few dodecagonal numbers are:
: 0, 1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 7 ...
*
142,857 =
Kaprekar number
In mathematics, a natural number in a given number base is a p-Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has p digits, that add up to the original number. The numbers are n ...
, smallest
cyclic number
A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the six-digit number 142857, whose first six integer multiples are
:142857 × 1 = 142857
:14 ...
in
decimal.
*
144,000
144,000 is a natural number. It has significance in various religious movements and ancient prophetic belief systems.
Religion Christianity
Book of Revelation
The number 144,000 appears three times in the Book of Revelation:
* Revelation 7:3–8 ...
= number with religious significance
* 147,640 = Keith number
* 148,149 = Kaprekar number
* 152,381 =
unique prime
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737.
Like all rational numbers, the reciprocals of primes have repeating decimal represen ...
in
base 20
vigesimal () or base-20 (base-score) numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). ''Vigesimal'' is derived from the Latin adjective '' vicesimus'', meaning 'twentieth'.
Places
In ...
* 156,146 = Keith number
* 160,000 = 20
4
* 161,051 = 11
5
* 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.
* 173,600 = harmonic divisor number
* 174,680 = Keith number
* 174,763 =
Wagstaff prime
In number theory, a Wagstaff prime is a prime number of the form
:
where ''p'' is an odd prime. Wagstaff primes are named after the mathematician Samuel S. Wagstaff Jr.; the prime pages credit François Morain for naming them in a lecture at the ...
* 177,147 = 3
11
* 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
* 183,186 = Keith number
* 183,231 = number of
partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a bina ...
with 9 unlabeled elements
* 187,110 = Kaprekar number
* 194,481 = 21
4
* 195,025 =
Pell number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , an ...
,
Markov number
* 196,418 = Fibonacci number,
Markov number
* 196,560 = the
kissing number
In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement o ...
in 24 dimensions
* 196,883 = the dimension of the smallest nontrivial
irreducible representation of the
Monster group
In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order
24632059761121331719232931414759 ...
* 196,884 = the coefficient of ''q'' in the
Fourier series expansion of the
j-invariant
In mathematics, Felix Klein's -invariant or function, regarded as a function of a complex variable , is a modular function of weight zero for defined on the upper half-plane of complex numbers. It is the unique such function which is hol ...
. The adjacency of 196883 and 196884 was important in suggesting
monstrous moonshine
In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group ''M'' and modular functions, in particular, the ''j'' function. The term was coined by John Conway and Simon P. Norton in 1979. ...
.
* 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
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
(see also
parsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, an ...
), since = 206,264.806...
* 207,360 = highly totient number
* 208,012 = the
Catalan number
In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Ca ...
''C''
12
* 208,335 = the largest number to be both
triangular
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- collinea ...
and
square pyramidal
In molecular geometry, square pyramidal geometry describes the shape of certain Chemical compound, compounds with the formula where L is a ligand. If the ligand atoms were connected, the resulting shape would be that of a Square pyramid, pyram ...
* 208,495 = Kaprekar number
* 212,159 = smallest unprimeable number ending in 1, 3, 7 or 9
* 221,760 = highly composite number
* 222,222 =
repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit.
Example ...
* 227,475 =
Riordan number
* 234,256 = 22
4
* 237,510 = harmonic divisor number
* 238,591 = number of free 13-ominoes
* 241,920 = highly totient number
* 242,060 = harmonic divisor number
* 248,832 = 100,000
12, AKA a gross-great-gross (100
12 great-grosses);12
5, the smallest fifth power that can be represented as the sum of only 6 fifth powers: 12
5 = 4
5 + 5
5 + 6
5 + 7
5 + 9
5 + 11
5
* 262,144 = 2
18;
exponential factorial of 4; a
superperfect number
* 262,468 = Leyland number
* 268,705 = Leyland number
* 274,177 = prime factor of the
Fermat number
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form
:F_ = 2^ + 1,
where ''n'' is a non-negative integer. The first few Fermat numbers are:
: 3, 5, 17, 257, 65537, 42949672 ...
''F''
6
* 275,807/195,025 ≈
√2
* 277,200 = highly composite number
* 279,841 = 23
4
* 279,936 = 6
7
* 280,859 = a
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
whose
square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
78881777881 is tridigital
* 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
* 317,811 = Fibonacci number
* 318,682 = Kaprekar number
* 325,878 = Fine number
* 326,981 =
alternating factorial
* 329,967 = Kaprekar number
* 331,776 = 24
4
* 332,640 = highly composite number;
harmonic divisor number
* 333,333 = repdigit
* 333,667 =
sexy prime
In number theory, sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and .
The term "sexy prime" is a pun stemming from the Latin word for six: .
If o ...
and
unique prime
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737.
Like all rational numbers, the reciprocals of primes have repeating decimal represen ...
* 333,673 = sexy prime with 333,679
* 333,679 = sexy prime with 333,673
* 337,500 = 2
2 × 3
3 × 5
5
* 351,351 = only known odd
abundant number
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. Th ...
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
* 360,360 = harmonic divisor number;
the smallest number divisible by all of the numbers 1 through 15
* 362,880 = 9!, highly totient number
* 370,261 = first prime followed by a
prime gap
A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g'n'' or ''g''(''p'n'') is the difference between the (''n'' + 1)-th and the
''n''-th prime numbers, i.e.
:g_n = p_ - p_n.\
W ...
of over 100
* 371,293 = 13
5, palindromic in base 12 (15AA51
12)
* 389,305 =
self-descriptive number
In mathematics, a self-descriptive number is an integer ''m'' that in a given base ''b'' is ''b'' digits long in which each digit ''d'' at position ''n'' (the most significant digit being at position 0 and the least significant at position ''b'' ...
in base 7
* 390,313 = Kaprekar number
* 390,625 = 5
8
* 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
The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base. The number twelve (that is, the number written as "12" in the decimal numerical system) is instead wr ...
* 437,760 to 440,319 = any of these numbers will cause the
Apple II+ and
Apple IIe
The Apple IIe (styled as Apple //e) is the third model in the Apple II series of personal computers produced by Apple Computer. The ''e'' in the name stands for ''enhanced'', referring to the fact that several popular features were now built-in ...
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 = 26
4
* 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 In mathematics, a Riesel number is an odd natural number ''k'' for which k\times2^n-1 is composite for all natural numbers ''n'' . In other words, when ''k'' is a Riesel number, all members of the following set are composite:
:\left\.
If the for ...
* 510,510 = the product of the first seven prime numbers, thus the seventh
primorial. It is also the product of four consecutive
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
s—13, 21, 34, 55, the highest such sequence of any length to be also a primorial. And it is a double
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
, the sum of all even numbers from 0 to 1428.
* 514,229 =
Fibonacci prime
A Fibonacci prime is a Fibonacci number that is prime, a type of integer sequence prime.
The first Fibonacci primes are :
: 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, ....
Known Fibonacci primes
It is not known whet ...
,
Markov prime
* 518,859 =
little Schroeder number
* 524,287 = Mersenne prime
* 524,288 = 2
19
* 524,649 = Leyland number
* 525,600 = minutes in a non-leap year
* 527,040 = minutes in a leap year
* 531,441 = 3
12
* 533,169 = Leyland number
* 533,170 = Kaprekar number
* 537,824 = 14
5
* 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 = 28
4
* 625,992 =
Riordan number
* 646,018 = Markov number
* 664,579 = the amount of primes under 10,000,000 there are
* 665,280 = highly composite number
* 665,857/470,832 ≈
√2
* 666,666 = repdigit
* 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 = 29
4
* 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 = 90
3
* 739,397 = largest prime that is both right- and left-
truncatable.
* 742,900 = Catalan number
* 753,480 = harmonic divisor number
* 759,375 = 15
5
* 765,623 =
emirp
An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as e ...
,
Friedman prime 5
6 × 7
2 − 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
* 799,999 = prime number.
800,000 to 899,999
* 810,000 = 30
4
* 823,543 = 7
7
* 825,265 = smallest
Carmichael number
In number theory, a Carmichael number is a composite number n, which in modular arithmetic satisfies the congruence relation:
:b^n\equiv b\pmod
for all integers b. The relation may also be expressed in the form:
:b^\equiv 1\pmod.
for all integers ...
with 5 prime factors
* 832,040 = Fibonacci number
* 853,467 = Motzkin number
* 857,375 = 95
3
* 873,612 = 1
1 + 2
2 + 3
3 + 4
4 + 5
5 + 6
6 + 7
7
* 888,888 = repdigit
* 890,625 = 1-
automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square "ends" in the same digits as the number itself.
Definition and properties
Given a number base b, a natura ...
[
]
900,000 to 999,999
* 900,001 = prime number
* 901,971 = number of free 14-ominoes
* 909,091 = unique prime
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737.
Like all rational numbers, the reciprocals of primes have repeating decimal represen ...
in base 10
* 923,521 = 314
* 925,765 = Markov number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation
:x^2 + y^2 + z^2 = 3xyz,\,
studied by .
The first few Markov numbers are
: 1, 2, 5, 13, 29, 34, 89 ...
* 925,993 = Keith number
In number theory, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number n in a given number base b with k digits such that when a sequence is created such that the first k terms are the k digits of n and ...
* 950,976 = harmonic divisor number
In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are:
: 1, 6, 2 ...
* 967,680 = highly totient number
* 998,001 = the reciprocal of this number, in its expanded form, lists all three-digit numbers in order except 998.
* 998,991 = highest triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
with 6 digits and the 1,413th triangular number
* 999,983 = largest 6-digit prime number
* 999,999 = repdigit. Rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all rat ...
s with denominators 7 and 13 have 6-digit repetend
A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if an ...
s 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, largest number in English not containing the letter 'l' in its name.
Prime numbers
Increments of 105 from zero
0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by multiplying digits to the left of 0 by the radix, usual ...
through a million have the following prime counts:
*9,592 primes between 0 and 100,000.
:99,991 is the largest prime number less than 100,000.
*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
Year 185 (Roman numerals, CLXXXV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Lascivius and Atilius (or, less frequently, year 938 ...
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 118 118 may refer to:
*118 (number)
*AD 118
*118 BC
*118 (TV series)
*118 (film)
*118 (Tees) Corps Engineer Regiment
*118 (Tees) Field Squadron, Royal Engineers
See also
*11/8 (disambiguation)
*Oganesson
Oganesson is a synthetic chemical element wi ...
primes from the previous range.
: 7,560 is the twentieth highly composite number
__FORCETOC__
A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...
.
:599,999 is prime.
*7,445 primes between 600,000 and 700,000.
:A difference of 115 115 may refer to:
* 115 (number), the number
* AD 115, a year in the 2nd century AD
* 115 BC, a year in the 2nd century BC
* 115 (Hampshire Fortress) Corps Engineer Regiment, Royal Engineers, a unit in the UK Territorial Army
* 115 (Leicestershire) ...
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
One million (1,000,000), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian ''millione'' (''milione'' in modern Italian), from ''mille'', "thousand", plus the au ...
.
: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.[
: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).]
Notes
References
{{DEFAULTSORT:100000
Integers