700 (number)

This article is about the numbers 700 through 799; for each individual number, see its section below.

700 (seven hundred) is the natural number following 699 and preceding 701.

← 699 700 701 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	seven hundred
Ordinal	700th (seven hundredth)
Factorization	22 × 52 × 7
Greek numeral	Ψ´
Roman numeral	DCC, dcc
Binary	10101111002
Ternary	2212213
Senary	31246
Octal	12748
Duodecimal	4A412
Hexadecimal	2BC16
Armenian	Չ
Hebrew	ת"ש / ן
Babylonian cuneiform	𒌋𒐕𒐏
Egyptian hieroglyph	𓍨

It is a composite number and the sum of four consecutive primes (167 + 173 + 179 + 181).

Integers from 701 to 799

Nearly all of the palindromic integers between 700 and 800 (i.e. nearly all numbers in this range that have both the hundreds and units digit be 7) are used as model numbers for Boeing Commercial Airplanes.

700s

701

701 is:

• a prime number
• the sum of three consecutive primes (229 + 233 + 239)
• a Chen prime
• an Eisenstein prime with no imaginary part

702

702 = 2 × 3³ × 13. It is:

• a pronic number
• a nontotient
• a Harshad number

703

703 = 19 × 37. It is:

• the 37th triangular number
• a hexagonal number
• the smallest number requiring 73 fifth powers for Waring representation
• a Kaprekar number

Other fields:

• a number commonly found in the formula for body mass index

704

704 = 2⁶ × 11. It is:

• a Harshad number
• a lazy caterer number (sequence A000124 in the OEIS)

705

705 = 3 × 5 × 47. It is:

• a sphenic number
• the smallest Bruckman-Lucas pseudoprime (sequence A005845 in the OEIS)

706

706 = 2 × 353. It is:

• a nontotient
• a Smith number

707

707 = 7 × 101. It is:

• the sum of five consecutive primes (131 + 137 + 139 + 149 + 151)
• a palindromic number
• the number of lattice paths from (0,0) to (5,5) with steps (0,1), (1,0) and, when on the diagonal, (1,1).

708

708 = 2² × 3 × 59. It is the number of partitions of 28 that do not contain 1 as a part.

709

709 is:

• a prime number
• a happy number

It is the seventh in the series 2, 3, 5, 11, 31, 127, 709 where each number is the nth prime with n being the number preceding it in the series, therefore, it is a prime index number.

710s

710

710 = 2 × 5 × 71. It is:

• a sphenic number
• a nontotient
• the number of forests with 11 vertices

711

711 = 3² × 79. It is:

• a Harshad number
• the number of planar Berge perfect graphs on 7 nodes

It is also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.

712

712 = 2³ × 89. It is:

• a refactorable number
• the sum of the first twenty-one primes
• the totient sum for first 48 integers.

It is the largest known number such that it and its 8th power (66,045,000,696,445,844,586,496) have no common digits.

713

713 = 23 × 31. It is a Blum integer.

In Judaism there are 713 letters on a Mezuzah scroll.

714

714 = 2 × 3 × 7 × 17. It is:

• a nontotient
• a balanced number
• a member of a Ruth–Aaron pair (either definition)
• the sum of twelve consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83)

The product of 714 and 715 is the product of the first 7 prime numbers (2, 3, 5, 7, 11, 13, and 17).

Other fields:

• It s an area code for Orange County, California.
• Flight 714 to Sidney is a Tintin graphic novel.
• 714 is the badge number of Sergeant Joe Friday.

715

715 = 5 × 11 × 13. It is:

• a sphenic number
• a pentagonal number
• a Harshad number
• a member of Ruth-Aaron pair (either definition)

It is a pentatope number because 713=${\tbinom {13}{4}}$.

716

716 = 2² × 179.

717

717 = 3 × 239. It is a palindromic number.

718

718 = 2 × 359.

719

719 is:

• a prime number
• a factorial prime (6! − 1)
• a Sophie Germain prime
• a safe prime
• a Chen prime
• an Eisenstein prime with no imaginary part
• the sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113)

720s

720

Main article: 720 (number)

721

721 = 7 × 103. It is:

• a centered hexagonal number
• the sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101)
• the smallest number that is the difference of two positive cubes in two ways

722

722 = 2 × 19². It is:

• a nontotient
• the number of odd parts in all partitions of 15
• the area of a square with diagonal 38

723

723 = 3 × 241. It is the side length of an almost-equilateral Heronian triangle.

724

724 = 2² × 181. It is:

• a nontotient
• the sum of four consecutive primes (173 + 179 + 181 + 191)
• the sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137)
• the side length of an almost-equilateral Heronian triangle
• the number of n-queens problem solutions for n = 10

725

725 = 5² × 29. It is the side length of an almost-equilateral Heronian triangle.

726

726 = 2 × 3 × 11².It is a pentagonal pyramidal number.

727

727 is:

• a prime number
• a palindromic prime
• a lucky prime

728

728 = 2³ × 7 × 13. It is:

• a nontotient
• a Smith number
• a cabtaxi number
• the number of cubes of edge length 1 required to make a hollow cube of edge length 12
• the number of connected graphs on 5 labelled vertices

Also:

• 728!! - 1 is prime.
• 728⁶⁴ + 1 is prime.

729

729 = 27² = 9³ = 3⁶.

• the square of 27, and the cube of 9, the sixth power of three, and because of these properties, a perfect totient number
• the largest three-digit cube (9 x 9 x 9)
• the only three-digit sixth power (3 x 3 x 3 x 3 x 3 x 3)
• a centered octagonal number
• a Smith number

A philosopher king's pleasure is 729 times a tyrant's pleasure according to Plato in the Republic.

730s

730

730 = 2 × 5 × 73. It is:

• a sphenic number
• a nontotient
• a Harshad number
• the number of generalized weak orders on 5 points

731

731 = 17 × 43. It is:

• the sum of three consecutive primes (239 + 241 + 251)
• the number of Euler trees with total weight 7

732

732 = 2² × 3 × 61. It is:

• a Harshad number
• the number of collections of subsets of {1, 2, 3, 4} that are closed under union and intersection
• the sum of eight consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107)
• the sum of ten consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97)

733

733 is:

• a prime number
• a balanced prime
• a permutable prime, and thus an emirp
• the sum of five consecutive primes (137 + 139 + 149 + 151 + 157)

734

734 = 2 × 367. It is:

• a nontotient
• the number of traceable graphs on 7 nodes

735

735 = 3 × 5 × 7².It is:

• a Harshad number
• a Zuckerman number
• the smallest number such that uses the same digits as its distinct prime factors

736

736 = 2⁵ × 23. It is:

• a centered heptagonal number
• a happy number
• a Harshad number
• a nice Friedman number since 736 = 7 + 3⁶

737

737 = 11 × 67. It is:

• a palindromic number
• a blum integer

738

738 = 2 × 3² × 41. It is a Harshad number.

739

739 is:

• a prime number
• a lucky prime
• a prime index prime
• a happy number
• a strictly non-palindromic number

740s

740

740 = 2² × 5 × 37. It is:

• a nontotient
• the number of connected square free graphs on 9 nodes

741

741 = 3 × 13 × 19. It is:

• a sphenic number
• the 38th triangular number

742

742 = 2 × 7 × 53. It is:

• a sphenic number
• a decagonal number
• an icosahedral number.
• a lazy caterer number (sequence A000124 in the OEIS)
• the number of partitions of 30 into divisors of 30.
• the smallest number that is one more than triple its reverse.

743

Main article: 743 (number)

744

Main article: 744 (number)

745

745 = 5 × 149. There are 745 non-connected simple labeled graphs covering 6 vertices.

746

746 = 2 × 373.

It is a nontotient. There are 746 non-normal semi-magic squares with sum of entries equal to 6.

746=1⁵ + 2⁴ + 3⁶ = 1⁷ + 2⁴ + 3⁶.

747

747 = 3² × 83. It is a palindromic number.

747=$\left\lfloor {\frac {4^{23}}{3^{23}}}\right\rfloor$

748

748 = 2² × 11 × 17. It is:

• a nontotient
• a happy number
• a primitive abundant number

749

749 = 7 × 107. It is:

• a blum integer
• the sum of three consecutive primes (241 + 251 + 257)

750s

750

750 = 2 × 3 × 5³. It is an enneagonal number.

751

751 is:

• a prime number

• a Chen prime

• an emirp

752

752 = 2⁴ × 47. It is a nontotient. There are 752 partitions of 11 into parts of 2 kinds

753

753 = 3 × 251. It is a blum integer.

754

754 = 2 × 13 × 29. It is:

• a sphenic number
• a nontotient
• the totient sum for first 49 integers

There are 754 different ways to divide a 10 × 10 square into sub-squares.

755

755 = 5 × 151. There are 755 vertices in a regular drawing of the complete bipartite graph K_9,9.

756

756 = 2² × 3³ × 7. It is:

• a pronic number
• a Harshad number
• the sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139)

757

757 is:

• a prime number
• a palindromic prime
• a happy number
• the sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127)

"The 757" is a local nickname for the Hampton Roads area in the U.S. state of Virginia, derived from the telephone area code that covers almost all of the metropolitan area.

758

758 = 2 × 379. It is:

• a nontotient
• a prime number of measurement

759

759 = 3 × 11 × 23. It is:

• a sphenic number
• the sum of five consecutive primes (139 + 149 + 151 + 157 + 163)
• a q-Fibonacci number for q=3

760s

760

760 = 2³ × 5 × 19.

It is a centered triangular number. There are 760 fixed heptominoes.

761

761 is:

• a prime number,
• an emirp,
• a Sophie Germain prime,
• a Chen prime,
• an Eisenstein prime with no imaginary part
• a centered square number

762

762 = 2 × 3 × 127. It is:

• a sphenic number
• a nontotient
• a Smith number
• an admirable number
• the sum of four consecutive primes (181 + 191 + 193 + 197)

There are 762 1's in all partitions of 25 into odd parts There are Six nines in the decimal representation of pi after the 762nd digit.

763

763 = 7 × 109.

It is the sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103). There are 763 degree-8 permutations of order exactly 2.

764

764 = 2² × 191. It is a telephone number.

765

765=3² × 5 × 17.

It is an octagonal pyramidal number

It is a Japanese word-play for Namco.

766

766 = 2 × 383. It is:

• a centered pentagonal number
• a nontotient
• the sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)

767

767 = 13 × 59. It is

• a Thabit number (2⁸ × 3 − 1)
• a palindromic number

768

768 = 2⁸ × 3. It is the sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109).

769

769 is:

• a prime number
• a Chen prime
• a lucky prime
• a Proth prime

770s

770

770 = 2 × 5 × 7 × 11. It is:

• a nontotient
• a Harshad number

$\sum _{n=0}^{10}770^{n}$ is prime

Other fields:

It holds special importance in the Chabad-Lubavitch Hasidic movement.

771

771 = 3 × 257.

It is sum of three consecutive primes in arithmetic progression (251 + 257 + 263). Since 771 is the product of the distinct Fermat primes 3 and 257, a regular polygon with 771 sides can be constructed using compass and straightedge, and $\cos \left({\frac {2\pi }{771}}\right)$ can be written in terms of square roots.

772

772 = 2² × 193.

772!!!!!!+1 is prime.

773

773 is:

• a prime number
• an Eisenstein prime with no imaginary part
• a prime index prime
• a tetranacci number
• the sum of the number of cells that make up the convex, regular 4-polytopes

774

774 = 2 × 3² × 43. It is:

• a nontotient
• the totient sum for first 50 integers
• a Harshad number

775

775 = 5² × 31. It is a member of the Mian–Chowla sequence

776

776 = 2³ × 97.

It is a refactorable number. There are 776 compositions of 6 whose parts equal to q can be of q² kinds.

777

Main article: 777 (number)

778

778 = 2 × 389. It is:

• a nontotient
• a Smith number

779

779 = 19 × 41. It is a highly cototient number.

780s

780

780 = 2² × 3 × 5 × 13. It is

• a hexagonal number
• a Harshad number
• the 39th triangular number
• the sum of four consecutive primes in a quadruplet (191, 193, 197, and 199)
• the sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101),

780 and 990 are the fourth smallest pair of triangular numbers whose sum and difference (1770 and 210) are also triangular.

781

781 = 11 × 71. It is:

• a zero of the Mertens function
• a lazy caterer number (sequence A000124 in the OEIS)
• the sum of powers of 5/repdigit in base 5 (11111)

782

782 = 2 × 17 × 23. It is

• a sphenic number
• a nontotient
• a pentagonal number
• a Harshad number

783

783 = 3³ × 29. It is a heptagonal number.

784

784 = 2⁴ × 7². It is a happy number.

Since 784=28², 784 is a perfect square. It is the sum of the cubes of the first seven positive integers; $1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}+7^{3}=784$.

785

785 = 5 × 157. It is a zero of the Mertens function. There are 785 series-reduced planted trees with 6 leaves of 2 colors.

786

Main article: 786 (number)

787

787 is:

• a prime number
• a Chen prime
• a lucky prime
• a palindromic prime
• the sum of five consecutive primes (149 + 151 + 157 + 163 + 167)

788

788 = 2² × 197.

It is a nontotient. There are 788 compositions of 12 into parts with distinct multiplicities.

789

789 = 3 × 263. It is:

• a Blum integer
• the sum of three consecutive primes (257 + 263 + 269)

790s

790

790 = 2 × 5 × 79. It is:

• a sphenic number
• a nontotient
• an aspiring number
• the aliquot sum of 1574
• a Harshad number in bases 2, 7, 14 and 16

791

791 = 7 × 113. It is:

• a centered tetrahedral number
• the sum of the first twenty-two primes
• the sum of seven consecutive primes (101 + 103 + 107 + 109 + 113 + 127 + 131)

792

792 = 2³ × 3² × 11. It is:

• a Harshad number
• the sum of the nontriangular numbers between successive triangular numbers

There are 792 integer partitions of 21.

792=${\tbinom {12}{5}}$, a binomial coefficent.

793

793 = 13 × 61. It is:

• a zero of the Mertens function
• a star number
• a happy number

794

794 = 2 × 397. It is a nontotient.

794= 1⁶ + 2⁶ + 3⁶.

795

795 = 3 × 5 × 53. It is:

• a sphenic number
• a zero of the Mertens function

There are 795 permutations of length 7 with 2 consecutive ascending pairs.

796

796 = 2² × 199. It is:

• a zero of the Mertens function
• the sum of six consecutive primes (113 + 127 + 131 + 137 + 139 + 149)

797

• 797 is:
• a prime number
• a Chen prime
• an Eisenstein prime with no imaginary part
• a palindromic prime
• a two-sided prime
• a prime index prime.

798

• 798 = 2 × 3 × 7 × 19. It is:
• a zero of the Mertens function
• a nontotient
• the product of primes indexed by the prime exponents of 10!

799

799 = 17 × 47. It is the smallest number with digit sum 25