4000 (four 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 n ...
following
3999 and preceding 4001. It is a
decagonal number
A decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal number ...
.
Selected numbers in the range 4001–4999
4001 to 4099
* 4005 –
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 in ...
* 4007 –
safe prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +  ...
* 4010 –
magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...
of ''n'' × ''n'' normal
magic square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
and
''n''-queens problem for ''n'' = 20.
* 4013 –
balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p_n, where is it ...
* 4019 –
Sophie Germain prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +  ...
* 4027 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4028 – sum of the first 45 primes
* 4030 – third
weird number
In number theory, a weird number is a natural number that is abundant but not semiperfect.
In other words, the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those diviso ...
* 4031 – sum of the cubes of the first six primes
* 4032 –
pronic number A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...
* 4033 – sixth
super-Poulet number A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor ''d'' divides
:2''d'' − 2.
For example, 341 is a super-Poulet number: it has positive divisors and we have:
:(211 - 2) / 11 = 2046 / 11 = 186
:(231 - 2 ...
;
strong pseudoprime A strong pseudoprime is a composite number that passes the Miller–Rabin primality test.
All prime numbers pass this test, but a small fraction of composites also pass, making them "pseudoprimes".
Unlike the Fermat pseudoprimes, for which there ex ...
in base 2
* 4060 –
tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is,
...
* 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 and 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. The ...
; number of divisors in the sum of the fifth and largest known
unitary perfect number
A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself (a divisor ''d'' of a number ''n'' is a unitary divisor if ''d'' and ''n''/''d'' share no common factors). Some perfect ...
, largest
Ramanujan–Nagell number of the form
.
* 4096 = 64
2 = 16
3 = 8
4 = 4
6 =
212, the smallest number with exactly 13 divisors, a
superperfect number In mathematics, a superperfect number is a positive integer ''n'' that satisfies
:\sigma^2(n)=\sigma(\sigma(n))=2n\, ,
where σ is the divisor summatory function. Superperfect numbers are a generalization of perfect numbers. The term was coined b ...
4100 to 4199
*
4104 = 2
3 + 16
3 = 9
3 + 15
3
* 4127 – safe prime
* 4133 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4139 – safe prime
* 4140 –
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 ...
* 4141 –
centered square number
In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each cen ...
* 4147 – 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
:142 ...
in
duodecimal
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 wri ...
represented in
base-12
The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using 12 (number), twelve as its radix, base. The number twelve (that is, the number written as "12" in the decimal numerical syste ...
notation as 2497
12.
2×4147
dez = 4972
123×4147
dez = 7249
124×4147
dez = 9724
12
* 4153 – super-prime
* 4160 – pronic number
* 4166 –
centered heptagonal number
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by ...
,
* 4167 = 7! − 6! − 5! − 4! − 3! − 2! − 1!, number of planar partitions of 14
* 4169 – a number of points of norm n = n in cubic lattice
* 4177 – prime of the form 2p-1
* 4181 –
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 ...
,
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 ...
* 4186 – triangular number
* 4187 – factor of
R13, also the record number of wickets taken in
first-class cricket
First-class cricket, along with List A cricket and Twenty20 cricket, is one of the highest-standard forms of cricket. A first-class match is one of three or more days' scheduled duration between two sides of eleven players each and is officiall ...
by
Wilfred Rhodes
Wilfred Rhodes (29 October 1877 – 8 July 1973) was an English professional cricketer who played 58 Test matches for England between 1899 and 1930. In Tests, Rhodes took 127 wickets and scored 2,325 runs, becoming the first Englishman t ...
.
* 4199 –
highly cototient number In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation
:x - \phi(x) = k
than any other integer below k and above 1. Here, \phi is Euler's totient fun ...
,
product of three consecutive primes
4200 to 4299
* 4200 –
nonagonal number A nonagonal number (or an enneagonal number) is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns inv ...
,
pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...
,
* 4210 – 11th
semi-meandric number In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges.
Meander
Given a fixed oriented lin ...
* 4211 –
Sophie Germain prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +  ...
* 4213 –
Riordan number
* 4217 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...
* 4219 –
cuban prime
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''.
First series
This is the first of these equations:
:p = \frac,\ x = ...
of the form ''x'' = ''y'' + 1,
centered hexagonal number
In mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following ...
* 4225 = 65
2,
centered octagonal number
A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the od ...
* 4227 – sum of the first 46 primes
* 4240 –
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, ...
* 4257 – decagonal number
* 4259 – safe prime
* 4261 – prime of the form 2p-1
* 4271 – Sophie Germain prime
* 4273 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
,
number of non-isomorphic set-systems of weight 11
* 4278 – triangular number
* 4279 –
little Schroeder number
* 4283 – safe prime
* 4289 – highly cototient number
* 4290 – pronic number
4300 to 4399
* 4324 – 23rd
square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broa ...
* 4325 – centered square number
* 4339 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
,
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 pr ...
* 4349 – Sophie Germain prime
* 4356 = 66
2, sum of the cubes of the first eleven integers
* 4357 – prime of the form 2p-1
* 4359 –
perfect totient number In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number ''n'', apply it again to the resulting totient, and so on, until the number 1 is reached, ...
* 4369 – seventh
super-Poulet number A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor ''d'' divides
:2''d'' − 2.
For example, 341 is a super-Poulet number: it has positive divisors and we have:
:(211 - 2) / 11 = 2046 / 11 = 186
:(231 - 2 ...
* 4371 – triangular number
* 4373 – Sophie Germain prime
* 4374 –
3-smooth
In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × 5 ...
number (2×3
7)
* 4375 – perfect totient number (the smallest not divisible by 3)
* 4391 – Sophie Germain prime
* 4397 – Year of
Comet Hale–Bopp
Comet Hale–Bopp (formally designated C/1995 O1) is a comet that was one of the most widely observed of the 20th century and one of the brightest seen for many decades.
Alan Hale and Thomas Bopp discovered Comet Hale–Bopp separately ...
's return,
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
4400 to 4499
* 4400 – the number of missing persons in the sci-fi show ''
The 4400
''The 4400'' (pronounced "the forty-four hundred") is a science fiction television series produced by CBS Paramount Network Television in association with BSkyB, Renegade 83, and American Zoetrope for USA Network in the United States and Sky ...
''
* 4409 – Sophie Germain prime, highly cototient number,
balanced prime,
600th prime number
* 4410 – member of the
Padovan sequence
In number theory, the Padovan sequence is the sequence of integers ''P''(''n'') defined. by the initial values
:P(0)=P(1)=P(2)=1,
and the recurrence relation
:P(n)=P(n-2)+P(n-3).
The first few values of ''P''(''n'') are
:1, 1, 1, 2, 2, 3, 4, 5 ...
* 4411 – centered heptagonal number
* 4421 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
,
alternating factorial
Alternating may refer to:
Mathematics
* Alternating algebra, an algebra in which odd-grade elements square to zero
* Alternating form, a function formula in algebra
* Alternating group, the group of even permutations of a finite set
* Alternati ...
* 4422 – pronic number
* 4425 = 1
5 + 2
5 + 3
5 + 4
5 + 5
5
* 4438 – sum of the first 47 primes
* 4446 – nonagonal number
* 4447 –
cuban prime
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''.
First series
This is the first of these equations:
:p = \frac,\ x = ...
of the form ''x'' = ''y'' + 1
* 4457 – balanced prime
* 4463 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4465 – triangular number
* 4481 – Sophie Germain prime
* 4489 = 67
2, centered octagonal number
* 4495 –
tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is,
...
4500 to 4599
* 4503 – largest number not the sum of four or fewer squares of composites
* 4505 – fifth
Zeisel number A Zeisel number, named after Helmut Zeisel, is a square-free integer ''k'' with at least three prime factors which fall into the pattern
:p_x = ap_ + b
where ''a'' and ''b'' are some integer constants and ''x'' is the index number of each prime f ...
* 4513 – centered square number
* 4516 –
centered pentagonal number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the ...
* 4517 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
,
happy number
In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because ...
* 4522 – decagonal number
* 4547 – safe prime
* 4549 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4556 – pronic number
* 4560 – triangular number
* 4567 – super-prime
* 4579 –
octahedral number
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The ''n''th octahedral number O_n can be obtained by the formula:.
:O_n=.
The first few octahed ...
* 4597 – balanced prime
4600 to 4699
* 4607 –
Woodall number
In number theory, a Woodall number (''W'n'') is any natural number of the form
:W_n = n \cdot 2^n - 1
for some natural number ''n''. The first few Woodall numbers are:
:1, 7, 23, 63, 159, 383, 895, … .
History
Woodall numbers were first st ...
* 4608 –
3-smooth
In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × 5 ...
number (2
9×3
2)
* 4619 – highly cototient number
* 4621 – prime of the form 2p-1
* 4624 = 68
2
* 4641 –
magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...
of ''n'' × ''n'' normal
magic square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
and
''n''-queens problem for ''n'' = 21.
* 4655 – number of free
decominoes
* 4656 – triangular number
* 4657 – balanced prime
* 4661 – sum of the first 48 primes
* 4663 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
, centered heptagonal number
* 4679 – safe prime
* 4681 – eighth
super-Poulet number A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor ''d'' divides
:2''d'' − 2.
For example, 341 is a super-Poulet number: it has positive divisors and we have:
:(211 - 2) / 11 = 2046 / 11 = 186
:(231 - 2 ...
* 4688 – 2-
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 ...
* 4689 – sum of divisors and number of divisors are both triangular numbers
* 4691 – balanced prime
* 4692 – pronic number
* 4699 – nonagonal number
4700 to 4799
* 4703 –
safe prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +  ...
* 4705 = 48
2 + 49
2 = 17
2 + 18
2 + ... + 26
2, centered square number
* 4727 – sum of the squares of the first twelve primes
* 4731 –
centered pentagonal number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the ...
* 4733 – Sophie Germain prime
* 4753 – triangular number
* 4759 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4761 = 69
2, centered octagonal number
* 4769 = number of square (0,1)-matrices without zero rows and with exactly 5 entries equal to 1.
* 4787 – safe prime,
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4788 – 14th
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 ...
* 4793 – Sophie Germain prime
* 4795 – decagonal number
* 4799 – safe prime
4800 to 4899
* 4801 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
,
cuban prime
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''.
First series
This is the first of these equations:
:p = \frac,\ x = ...
of the form ''x'' = ''y'' + 2, smallest prime with a composite sum of digits in base 7
* 4830 – pronic number
* 4840 - square yards in an
acre
The acre is a unit of land area used in the imperial
Imperial is that which relates to an empire, emperor, or imperialism.
Imperial or The Imperial may also refer to:
Places
United States
* Imperial, California
* Imperial, Missouri
* Imp ...
* 4851 – triangular number,
pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...
* 4862 –
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 Cata ...
* 4871 – Sophie Germain prime
* 4877 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4879 – 11th
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 ...
* 4888 – sum of the first 49 primes
4900 to 4999
* 4900 = 70
2, the only
square-pyramidal 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 adj ...
other than
1
* 4901 – centered square number
* 4913 = 17
3
* 4919 – Sophie Germain prime, safe prime
* 4922 – centered heptagonal number
* 4933 –
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4941 –
centered cube number
A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equival ...
* 4943 –
Sophie Germain prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +  ...
,
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
* 4950 – triangular number, 12th
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 ...
* 4951 –
centered pentagonal number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the ...
* 4957 – sum of three and five consecutive primes (1637 + 1657 + 1663, 977 + 983 + 991 + 997 + 1009)
* 4959 – nonagonal number
* 4960 –
tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is,
...
;
greater of fourth pair of
Smith brothers
The Smith Brothers were makers of the first cough drops produced and advertised in the United States, becoming one of the most famous brands in the country in its day.
History
William Wallace Smith I (1830–1913) and Andrew Smith (1836–1895 ...
* 4970 – pronic number
* 4973 – the 666th prime
* 4991 –
Lucas–Carmichael number In mathematics, a Lucas–Carmichael number is a positive composite integer ''n'' such that
# if ''p'' is a prime factor of ''n'', then ''p'' + 1 is a factor of ''n'' + 1;
# ''n'' is odd and square-free.
The first condition resembles the Korselt's ...
* 4993 – balanced prime
* 4999 –
prime
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 ...
of the form
Prime numbers
There are 119
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 ...
s between 4000 and 5000:
:4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999
References
{{Integers, 10
Integers