# 700 (number)

| ||||
---|---|---|---|---|

Cardinal | seven hundred | |||

Ordinal | 700th (seven hundredth) | |||

Factorization | 2^{2}× 5^{2}× 7 | |||

Greek numeral | Ψ´ | |||

Roman numeral | DCC | |||

Binary | 1010111100_{2} | |||

Ternary | 221221_{3} | |||

Quaternary | 22330_{4} | |||

Quinary | 10300_{5} | |||

Senary | 3124_{6} | |||

Octal | 1274_{8} | |||

Duodecimal | 4A4_{12} | |||

Hexadecimal | 2BC_{16} | |||

Vigesimal | 1F0_{20} | |||

Base 36 | JG_{36} |

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

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

## Contents

## Integers from 701 to 799[edit]

### 700s[edit]

- 701 = prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime, Eisenstein prime with no imaginary part
- 702 = 2 × 3
^{3}× 13, pronic number,^{[1]}nontotient, Harshad number - 703 = 19 × 37, triangular number,
^{[2]}hexagonal number,^{[3]}smallest number requiring 73 fifth powers for Waring representation, Kaprekar number,^{[4]}area code for Northern Virginia along with 571, a number commonly found in the formula for body mass index - 704 = 2
^{6}× 11, Harshad number, area code for the Charlotte, NC area. - 705 = 3 × 5 × 47, sphenic number, smallest Lucas pseudoprime
- 706 = 2 × 353, nontotient, Smith number
^{[5]} - 707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151), palindromic number
- 708 = 2
^{2}× 3 × 59 - 709 = prime number; happy number.

### 710s[edit]

- 710 = 2 × 5 × 71, sphenic number, nontotient
- 711 = 3
^{2}× 79, Harshad number. Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing. - 712 = 2
^{3}× 89, sum of the first twenty-one primes, 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 = 23 × 31, main area code for Houston, TX. In Judaism there is 713 letters on a Mezuzah scroll.
- 714 = 2 × 3 × 7 × 17, sum of twelve consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), nontotient, member of Ruth–Aaron pair (either definition); the smallest number that uses the same digits in bases 2 and 5, area code for Orange County, California.
- 714 is the number of career home runs hit by Babe Ruth, a record that stood from his last home run on May 25, 1935 until being broken by Hank Aaron on April 8, 1974.
*Flight 714 to Sidney*is a Tintin graphic novel.- 714 is the badge number of Sergeant Joe Friday.

- 715 = 5 × 11 × 13, sphenic number, pentagonal number,
^{[6]}pentatope number ( binomial coefficient ),^{[7]}

Harshad number, member of Ruth-Aaron pair (either definition)

- 716 = 2
^{2}× 179, area code for Buffalo, NY - 717 = 3 × 239, palindromic number
- 718 = 2 × 359, area code for Brooklyn, NY and Bronx, NY
- 719 = prime number, factorial prime (6! − 1),
^{[8]}Sophie Germain prime,^{[9]}safe prime,^{[10]}sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part

### 720s[edit]

- 720 (
*seven hundred [and] twenty*)= 2^{4}× 3^{2}× 5.- 6 factorial, highly composite number, Harshad number in every base from binary to decimal, highly totient number.
- two round angles (= 2 × 360).
- five gross (= 500 duodecimal, 5 × 144).
- 241-gonal number.

- 721 = 7 × 103, sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), centered hexagonal number,
^{[11]}smallest number that is the difference of two positive cubes in two ways, - 722 = 2 × 19
^{2}, nontotient- G.722 is a freely available file format for audio file compression. The files are often named with the extension "722".

- 723 = 3 × 241
- 724 = 2
^{2}× 181, sum of four consecutive primes (173 + 179 + 181 + 191), sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137), nontotient- the number of
*n*-queens problem solutions for*n*= 10,

- the number of
- 725 = 5
^{2}× 29 - 726 = 2 × 3 × 11
^{2}, pentagonal pyramidal number^{[12]} - 727 = prime number, palindromic prime, lucky prime
^{[13]} - 728 = 2
^{3}× 7 × 13, nontotient, Smith number,^{[5]}cabtaxi number^{[14]} - 729 = 3
^{6}= 27^{2}.- the square of 27, and the cube of 9, and as a consequence of these properties, a perfect totient number.
^{[15]} - centered octagonal number,
^{[16]}Smith number^{[5]} - the number of times a philosopher's pleasure is greater than a tyrant's pleasure according to Plato in the Republic
- the largest three digit cube. (9 x 9 x 9)
- the largest three digit sixth power. (3 x 3 x 3 x 3 x 3 x 3)

- the square of 27, and the cube of 9, and as a consequence of these properties, a perfect totient number.

### 730s[edit]

- 730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number, happy number
- 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251)
- 732 = 2
^{2}× 3 × 61, sum of eight consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), sum of ten consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), Harshad number - 733 = prime number, balanced prime,
^{[17]}permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157) - 734 = 2 × 367, nontotient
- 735 = 3 × 5 × 7
^{2}, Harshad number, Zuckerman number, smallest number such that uses same digits as its distinct prime factors - 736 = 2
^{5}× 23, centered heptagonal number,^{[18]}nice Friedman number since 736 = 7 + 3^{6}, Harshad number - 737 = 11 × 67, palindromic number, Boeing 737 jet airliner.
- 738 = 2 × 3
^{2}× 41, Harshad number, designation for a Boeing 737-800 jet airliner. - 739 = prime number, strictly non-palindromic number,
^{[19]}lucky prime,^{[13]}happy number

### 740s[edit]

- 740 = 2
^{2}× 5 × 37, nontotient - 741 = 3 × 13 × 19, sphenic number, triangular number
^{[2]} - 742 = 2 × 7 × 53, sphenic number, decagonal number.
^{[20]}It is the smallest number that is one more than triple its reverse.

- 743 = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part
- 744 = 2
^{3}× 3 × 31, sum of four consecutive primes (179 + 181 + 191 + 193). It is the coefficient of the first degree term of the expansion of Klein's j-invariant. Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebra*E*_{8}. - 745 = 5 × 149
- 746 = 2 × 373, nontotient
- 746 = 1
^{7}+ 2^{4}+ 3^{6}

- 746 = 1
- 747 = 3
^{2}× 83, palindromic number, model number of the Boeing 747, perhaps the most famous Boeing aircraft - 748 = 2
^{2}× 11 × 17, nontotient, happy number, primitive abundant number^{[21]} - 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257)

### 750s[edit]

- 750 = 2 × 3 × 5
^{3}, enneagonal number.^{[22]} - 751 = prime number, Chen prime
- 752 = 2
^{4}× 47, nontotient - 753 = 3 × 251
- 754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers
- 755 = 5 × 151. In 1976, Major League Baseball player Hank Aaron ended his career with a Major League record 755 home runs (record now held by Barry Bonds).
- 756 = 2
^{2}× 3^{3}× 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number,^{[1]}Harshad number - 757 = prime number, palindromic prime, sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127), happy number
- "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 = 2 × 379, nontotient
- 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163)

### 760s[edit]

- 760 = 2
^{3}× 5 × 19, centered triangular number^{[23]} - 761 = prime number, Sophie Germain prime,
^{[9]}Chen prime, Eisenstein prime with no imaginary part, centered square number^{[24]} - 762 = 2 × 3 × 127, sphenic number, sum of four consecutive primes (181 + 191 + 193 + 197), nontotient, Smith number,
^{[5]}see also Six nines in pi - 763 = 7 × 109, sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103)
- 764 = 2
^{2}× 191, telephone number^{[25]} - 765 = 3
^{2}× 5 × 17 - 766 = 2 × 383, centered pentagonal number,
^{[26]}nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), happy number - 767 = 13 × 59, Thabit number (2
^{8}× 3 − 1), palindromic number - 768 = 2
^{8}× 3, sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109) - 769 = prime number, Chen prime, lucky prime,
^{[13]}Proth prime^{[27]}

### 770s[edit]

- 770 = 2 × 5 × 7 × 11, nontotient, Harshad number
- Famous room party in New Orleans hotel room 770, giving the name to a well known science fiction fanzine called File 770
- Holds special importance in the Chabad-Lubavitch Hasidic movement.

- 771 = 3 × 257, 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 can be written in terms of square roots.
- 772 = 2
^{2}× 193 - 773 = prime number, Eisenstein prime with no imaginary part, tetranacci number
^{[28]} - 774 = 2 × 3
^{2}× 43, nontotient, totient sum for first 50 integers, Harshad number - 775 = 5
^{2}× 31, member of the Mian–Chowla sequence,^{[29]}happy number - 776 = 2
^{3}× 97

- 777 = 3 × 7 × 37, sphenic number, Harshad number, palindromic number, 3333 in senary (base 6) counting.
- The numbers 3 and 7 are considered both "perfect numbers" under Hebrew tradition.
^{[30]}^{[31]}777 is also found in the title of the book*777 and other Qabalistic writings of Aleister Crowley*.

- The numbers 3 and 7 are considered both "perfect numbers" under Hebrew tradition.
- 778 = 2 × 389, nontotient, Smith number
^{[5]} - 779 = 19 × 41, highly cototient number
^{[32]}

### 780s[edit]

- 780 = 2
^{2}× 3 × 5 × 13, sum of four consecutive primes in a quadruplet (191, 193, 197, and 199); sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), triangular number,^{[2]}hexagonal number,^{[3]}Harshad number- 780 and 990 are the fourth smallest pair of triangular numbers whose sum and difference (1770 and 210) are also triangular.

- 781 = 11 × 71, sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0
- 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,
^{[6]}Harshad number, also, 782 gear used by U.S. Marines - 783 = 3
^{3}× 29 - 784 = 2
^{4}× 7^{2}= 28^{2}= , the sum of the cubes of the first seven integers, happy number - 785 = 5 × 157, Mertens function(785) = 0

- 786 = 2 × 3 × 131, sphenic number. See also its use in Muslim numerological symbolism.
- 787 = prime number, sum of five consecutive primes (149 + 151 + 157 + 163 + 167), Chen prime, lucky prime,
^{[13]}palindromic prime. - 788 = 2
^{2}× 197, nontotient - 789 = 3 × 263, sum of three consecutive primes (257 + 263 + 269)

### 790s[edit]

- 790 = 2 × 5 × 79, sphenic number, nontotient
- 791 = 7 × 113, sum of the first twenty-two primes, sum of seven consecutive primes (101 + 103 + 107 + 109 + 113 + 127 + 131)
- 792 = 2
^{3}× 3^{2}× 11, number of partitions of 21,^{[33]}binomial coefficient , Harshad number - 793 = 13 × 61, Mertens function(793) = 0, star number,
^{[34]}happy number - 794 = 2 × 397, nontotient
- 795 = 3 × 5 × 53, Mertens function(795) = 0
- 796 = 2
^{2}× 199, sum of six consecutive primes (113 + 127 + 131 + 137 + 139 + 149), Mertens function(796) = 0 - 797 = prime number, Chen prime, Eisenstein prime with no imaginary part, palindromic prime
- 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient
- 799 = 17 × 47

## References[edit]

- ^
^{a}^{b}"Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. - ^
^{a}^{b}^{c}"Sloane's A000217 : Triangular numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. - ^
^{a}^{b}"Sloane's A000384 : Hexagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. **^**"Sloane's A006886 : Kaprekar numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{a}^{b}^{c}^{d}^{e}"Sloane's A006753 : Smith numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. - ^
^{a}^{b}"Sloane's A000326 : Pentagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. **^**"Sloane's A000332 : Binomial coefficient binomial(n,4)".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A088054 : Factorial primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{a}^{b}"Sloane's A005384 : Sophie Germain primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. **^**"Sloane's A005385 : Safe primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A003215 : Hex (or centered hexagonal) numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A002411 : Pentagonal pyramidal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.- ^
^{a}^{b}^{c}^{d}"Sloane's A031157 : Numbers that are both lucky and prime".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11. **^**"Sloane's A047696 : Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) cubes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A082897 : Perfect totient numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A006562 : Balanced primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A069099 : Centered heptagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A016038 : Strictly non-palindromic numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A001107 : 10-gonal (or decagonal) numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A091191 : Primitive abundant numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A005448 : Centered triangular numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A001844 : Centered square numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A000085 : Number of self-inverse permutations on n letters, also known as involutions".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A005891 : Centered pentagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A080076 : Proth primes".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A000078 : Tetranacci numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A005282 : Mian-Chowla sequence".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**Posner, Eliezer. "On the Meaning of Three". Chabad. Retrieved 2 July 2016.**^**Dennis, Geoffrey. "Judaism & Numbers". My Jewish Learning. Retrieved 2 July 2016.**^**"Sloane's A100827 : Highly cototient numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A000041 : a(n) = number of partitions of n".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.**^**"Sloane's A003154 : Centered 12-gonal numbers. Also star numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-11.