7000 (seven thousand) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 6999 and preceding 7001.

Selected numbers in the range 7001–7999

7001 to 7099

* 7021 –

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 ...

* 7043 –

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 +&nbs ...

* 7056 = 84² * 7057 – cuban prime of the form ''x'' = ''y'' + 1,

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. In other words, if prime numbers are matched ...

* 7073 –

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, ...

* 7079 – Sophie Germain prime,

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 +&nbs ...

7100 to 7199

* 7103 – Sophie Germain prime,

sexy prime In number theory, sexy primes are prime numbers that differ from each other by . For example, the numbers and are a pair of sexy primes, because both are prime and 11 - 5 = 6. The term "sexy prime" is a pun stemming from the Latin word for six ...

with 7109 * 7106 –

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 th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahedral ...

* 7109 –

, sexy prime with 7103 * 7121 – Sophie Germain prime * 7140 – triangular number, also a

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 ...

and hence = 3570 is also a triangular number,

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...

* 7141 - sum of the first 58 primes,

star number In mathematics, a star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n' ...

* 7151 – Sophie Germain prime * 7155 – number of 19-bead necklaces (turning over is allowed) where complements are equivalent * 7187 – safe prime * 7192 –

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 divi ...

* 7193 – Sophie Germain prime,

7200 to 7299

* 7200 –

pentagonal pyramidal number A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of s ...

* 7211 – Sophie Germain prime * 7225 = 85²,

centered octagonal number A centered octagonal number is a centered number, 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 th ...

* 7230 = 36² + 37² + 38² + 39² + 40² = 41² + 42² + 43² + 44² * 7246 –

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 ...

* 7247 – safe prime * 7260 – triangular number * 7267 –

decagonal number In mathematics, 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 ...

* 7272 –

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. For example, in ...

* 7283 –

* 7291 –

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 in ...

7300 to 7399

* 7310 -

* 7316 – number of 18-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed * 7338 – Fine number. * 7349 – Sophie Germain prime * 7351 –

, cuban prime of the form ''x'' = ''y'' + 1 * 7381 – triangular number * 7385 –

Keith number In recreational mathematics, 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 d ...

* 7396 = 86²

7400 to 7499

* 7417 –

* 7418 - sum of the first 59 primes * 7433 – Sophie Germain prime * 7471 –

centered cube number A centered cube number is a centered figurate number that counts the 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. Equivalently, it ...

* 7481 – super-prime, cousin prime * 7482 -

7500 to 7599

* 7503 – triangular number * 7523 –

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, the nth prime number p_n is a balanced ...

, safe prime,

* 7537 – prime of the form 2p-1 * 7541 – Sophie Germain prime * 7559 – safe prime * 7560 – the 20th

highly composite number A highly composite number is a positive integer that has more divisors than all smaller positive integers. If ''d''(''n'') denotes the number of divisors of a positive integer ''n'', then a positive integer ''N'' is highly composite if ''d''(' ...

* 7561 –

Markov prime 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, ...

star prime In mathematics, a star number is a centered number, centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' ...

* 7568 – centered heptagonal number * 7569 = 87², centered octagonal number * 7583 – balanced prime

7600 to 7699

* 7607 – safe prime,

* 7612 – decagonal number * 7614 – nonagonal number * 7626 – triangular number * 7643 – Sophie Germain prime, safe prime * 7647 – Keith number * 7649 – Sophie Germain prime,

* 7656 -

* 7691 – Sophie Germain prime * 7699 –

emirp An emirp (an anadrome of ''prime'') 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 emirp, ...

, sum of the first 60 primes, first prime above 281 to be the sum of the first k primes for some k

7700 to 7799

* 7703 – safe prime * 7710 = number of primitive polynomials of degree 17 over GF(2) * 7714 –

square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid (geometry), pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part ...

* 7727 – safe prime * 7739 – member of the

Padovan sequence In number theory, the Padovan sequence is the integer sequence, 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 ...

* 7741 = number of trees with 15 unlabeled nodes * 7744 = 88², square palindrome not ending in 0 * 7750 – triangular number * 7753 –

* 7770 – tetrahedral number * 7776 = 6⁵, number of primitive polynomials of degree 18 over GF(2) * 7777 – Kaprekar number,

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". Ex ...

7800 to 7899

* 7810 –

ISO/IEC 7810 International Organization for Standardization, ISO/International Electrotechnical Commission, IEC 7810 ''Identification cards — Physical characteristics'' is an international standard that defines the physical characteristics for identifica ...

is the

ISO The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries. Me ...

's standard for physical characteristics of identification cards * 7821 – n=6 value of

\sum_^n^

* 7823 – Sophie Germain prime, safe prime, balanced prime * 7825 –

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 mathematics, especially History of mathematics, historical and 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 diago ...

and

n-Queens Problem The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. ...

for ''n'' = 25. Also the first counterexample in the

Boolean Pythagorean triples problem The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue members. The Boolean Pythagorean triples problem w ...

. * 7832 -

* 7841 – Sophie Germain prime, balanced prime,

* 7875 – triangular number * 7883 – Sophie Germain prime, super-prime * 7897 – centered heptagonal number

7900 to 7999

* 7901 – Sophie Germain prime * 7909 – Keith number * 7912 – weird number * 7919 – 1000th prime number * 7920 – the order of the

Mathieu group In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups ''M''11, ''M''12, ''M''22, ''M''23 and ''M''24 introduced by . They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objec ...

M₁₁, the smallest

sporadic simple group In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups. A simpl ...

* 7921 = 89², centered octagonal number * 7944 – nonagonal number * 7957 –

super-Poulet number In number theory, 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 (1, 11, 31, 341), and we have: :(211 − 2) / 11 = 2 ...

* 7965 – decagonal number * 7979 –

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 func ...

* 7982 - sum of the first 61 primes * 7993 -

, reverse superstar prime

Prime numbers

There are 107

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), 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 ...

s between 7000 and 8000: :7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993

References

{{Integers, 10 Integers