700 (number)

← 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	2^2× 5^2× 7
Roman numeral	DCC
Binary	10101111002
Ternary	2212213
Quaternary	223304
Quinary	103005
Senary	31246
Octal	12748
Duodecimal	4A412
Hexadecimal	2BC16
Vigesimal	1F020
Base 36	JG36

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.

700 is also:

• The year AD, see 700.
• The decade beginning in the year 700 BC, see 700s BC.
• A television show that aired on the Christian Broadcasting Network, see The 700 Club.

700s

700 — see above

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701 prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime, Eisenstein prime with no imaginary part

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702 = 2 × 3³ × 13, pronic number,^[1] nontotient, Harshad number

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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

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704 = 2⁶ × 11, Harshad number, area code for the Charlotte, NC area.

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705 = 3 × 5 × 47, sphenic number, smallest Lucas pseudoprime

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706 = 2 × 353, nontotient, Smith number^[5]

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707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151), palindromic number

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708 = 2² × 3 × 59

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709 is a prime number. It is also a happy number.

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710 = 2 × 5 × 71, sphenic number, nontotient

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711 = 3² × 79, Harshad number. Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.

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712 = 2³ × 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.

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713 = 23 × 31, main area code for Houston, TX.

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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.

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715 = 5 × 11 × 13, sphenic number, pentagonal number,^[6] pentatope number ( binomial coefficient ${\tbinom {13}4}$ ),^[7] Harshad number, member of Ruth-Aaron pair (either definition)

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716 = 2² × 179, area code for Buffalo, NY

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717 = 3 × 239, palindromic number

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718 = 2 × 359, area code for Brooklyn, NY

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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

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720 (seven hundred [and] twenty)= 2⁴ × 3² × 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.

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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,

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722 = 2 × 19², nontotient

• G.722 is a freely available file format for audio file compression. The files are often named with the extension "722".

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723 = 3 × 241

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724 = 2² × 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,

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725 = 5² × 29

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726 = 2 × 3 × 11², pentagonal pyramidal number^[12]

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727 prime number, palindromic prime, lucky prime^[13]

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728 = 2³ × 7 × 13, nontotient, Smith number,^[5] cabtaxi number^[14]

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729 (seven hundred [and] twenty-nine) = 3⁶ = 27².

• 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)

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730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number, happy number

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731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251)

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732 = 2² × 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

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733 prime number, balanced prime,^[17] permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)

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734 = 2 × 367, nontotient

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735 = 3 × 5 × 7², Harshad number, Zuckerman number, smallest number such that uses same digits as its distinct prime factors

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736 = 2⁵ × 23, centered heptagonal number,^[18] nice Friedman number since 736 = 7 + 3⁶, Harshad number

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737 = 11 × 67, palindromic number, Boeing 737 jet airliner.

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738 = 2 × 3² × 41, Harshad number, designation for a Boeing 737-800 jet airliner.

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739 prime number, strictly non-palindromic number,^[19] lucky prime,^[13] happy number

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740 = 2² × 5 × 37, nontotient

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741 = 3 × 13 × 19, sphenic number, triangular number^[2]

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742 = 2 × 7 × 53, sphenic number, decagonal number.^[20] It is the smallest number that is one more than triple its reverse.

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743 prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part

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744 = 2³ × 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 E₈.

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745 = 5 × 149

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746 = 2 × 373, nontotient 746 = 1⁷ + 2⁴ + 3⁶

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747 = 3² × 83, palindromic number, model number of the Boeing 747, perhaps the most famous Boeing aircraft

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748 = 2² × 11 × 17, nontotient, happy number, primitive abundant number^[21]

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749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257)

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750 (seven hundred [and] fifty)= 2 × 3 × 5³, enneagonal number.^[22]

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751 prime number, Chen prime

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752 = 2⁴ × 47, nontotient

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753 = 3 × 251

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754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers

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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).

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756 = 2² × 3³ × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number,^[1] Harshad number

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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.

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758 = 2 × 379, nontotient

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759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163)

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760 = 2³ × 5 × 19, centered triangular number^[23]

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761 prime number, Sophie Germain prime,^[9] Chen prime, Eisenstein prime with no imaginary part, centered square number^[24]

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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

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763 = 7 × 109, sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103)

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764 = 2² × 191, telephone number^[25]

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765 = 3² × 5 × 17

• a Japanese word-play for Namco;

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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

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767 = 13 × 59, Thabit number (2⁸ × 3 − 1), palindromic number

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

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769 prime number, Chen prime, lucky prime,^[13] Proth prime^[27]

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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.

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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 $\cos\left(\frac{2\pi}{771}\right)$ can be written in terms of square roots.

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772 = 2² × 193

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773 prime number, Eisenstein prime with no imaginary part, tetranacci number^[28]

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774 = 2 × 3² × 43, nontotient, totient sum for first 50 integers, Harshad number

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775 = 5² × 31, member of the Mian–Chowla sequence,^[29] happy number

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776 = 2³ × 97

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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.

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778 = 2 × 389, nontotient, Smith number^[5]

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779 = 19 × 41, highly cototient number^[32]

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780 = 2² × 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.

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781 = 11 × 71, sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0

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782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,^[6] Harshad number, also, 782 gear used by U.S. Marines

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783 = 3³ × 29

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784 = 2⁴ × 7² = 28² = $1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}+7^{3}$, the sum of the cubes of the first seven integers, happy number

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785 = 5 × 157, Mertens function(785) = 0

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786 = 2 × 3 × 131, sphenic number. See also its use in Muslim numerological symbolism.

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787 prime number, sum of five consecutive primes (149 + 151 + 157 + 163 + 167), Chen prime, lucky prime,^[13] palindromic prime.

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788 = 2² × 197, nontotient

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789 = 3 × 263, sum of three consecutive primes (257 + 263 + 269)

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790 = 2 × 5 × 79, sphenic number, nontotient

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791 = 7 × 113, sum of the first twenty-two primes, sum of seven consecutive primes (101 + 103 + 107 + 109 + 113 + 127 + 131)

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792 = 2³ × 3² × 11, number of partitions of 21,^[33] binomial coefficient ${\tbinom {12}5}$, Harshad number

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793 = 13 × 61, Mertens function(793) = 0, star number,^[34] happy number

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794 = 2 × 397, nontotient

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795 = 3 × 5 × 53, Mertens function(795) = 0

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796 = 2² × 199, sum of six consecutive primes (113 + 127 + 131 + 137 + 139 + 149), Mertens function(796) = 0

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797 prime number, Chen prime, Eisenstein prime with no imaginary part, palindromic prime

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798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient

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799 = 17 × 47

References

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2. "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
3. "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
4. "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
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31. Dennis, Geoffrey. "Judaism & Numbers". My Jewish Learning. Retrieved 2 July 2016.
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