700 (number)
700 (seven hundred) is the natural number following 699 and preceding 701.
| ||||
---|---|---|---|---|
Cardinal | seven hundred | |||
Ordinal | 700th (seven hundredth) | |||
Factorization | 22 × 52 × 7 | |||
Greek numeral | Ψ´ | |||
Roman numeral | DCC | |||
Binary | 10101111002 | |||
Ternary | 2212213 | |||
Octal | 12748 | |||
Duodecimal | 4A412 | |||
Hexadecimal | 2BC16 |
It is the sum of four consecutive primes (167 + 173 + 179 + 181). It is a Harshad number.
Integers from 701 to 799
700s
- 701 = prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime, Eisenstein prime with no imaginary part
- 702 = 2 × 33 × 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 = 26 × 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 = 22 × 3 × 59
- 709 = prime number; happy number.
710s
- 710 = 2 × 5 × 71, sphenic number, nontotient
- 711 = 32 × 79, Harshad number. Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.
- 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.
- 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)
- The product of 714 and 715 is the product of the first 7 prime numbers (2, 3, 5, 7, 11, 13, and 17)
- 716 = 22 × 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
- 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.
- 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 × 192, 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 = 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,
- 725 = 52 × 29
- 726 = 2 × 3 × 112, pentagonal pyramidal number[12]
- 727 = prime number, palindromic prime, lucky prime[13]
- 728 = 23 × 7 × 13, nontotient, Smith number,[5] cabtaxi number[14]
- 729 = 36 = 272.
- the square of 27, and the cube of 9, the sixth power of three, 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 only three digit sixth power. (3 x 3 x 3 x 3 x 3 x 3)
730s
- 730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number, happy number
- 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251)
- 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
- 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 × 72, Harshad number, Zuckerman number, smallest number such that uses same digits as its distinct prime factors
- 736 = 25 × 23, centered heptagonal number,[18] nice Friedman number since 736 = 7 + 36, Harshad number
- 737 = 11 × 67, palindromic number, model number of the Boeing 737 jet airliner.
- 738 = 2 × 32 × 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
- 740 = 22 × 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 = 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.
- 745 = 5 × 149
- 746 = 2 × 373, nontotient
- 746 = 17 + 24 + 36
- 747 = 32 × 83, palindromic number, model number of the Boeing 747 jet airliner
- 748 = 22 × 11 × 17, nontotient, happy number, primitive abundant number[21]
- 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257)
750s
- 750 = 2 × 3 × 53, enneagonal number.[22]
- 751 = prime number, Chen prime
- 752 = 24 × 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 = 22 × 33 × 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
- 760 = 23 × 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 = 22 × 191, telephone number[25]
- 765 = 32 × 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 (28 × 3 − 1), palindromic number
- 768 = 28 × 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
- 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 = 22 × 193
- 773 = prime number, Eisenstein prime with no imaginary part, tetranacci number[28]
- 774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number
- 775 = 52 × 31, member of the Mian–Chowla sequence,[29] happy number
- 776 = 23 × 97
- 777 = 3 × 7 × 37, sphenic number, Harshad number, palindromic number, model number of the Boeing 777 jet airliner, 3333 in senary (base 6) counting.
- 778 = 2 × 389, nontotient, Smith number[5]
- 779 = 19 × 41, highly cototient number[32]
780s
- 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.
- 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 = 33 × 29
- 784 = 24 × 72 = 282 = , 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 = 22 × 197, nontotient
- 789 = 3 × 263, sum of three consecutive primes (257 + 263 + 269)
790s
- 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 = 23 × 32 × 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 = 22 × 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, two-sided_prime
- 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient
- 799 = 17 × 47
gollark: Hmm, that's old then.
gollark: Out of interest, what kernel version are you running?
gollark: Well, I'll just have to frantically duckduckgo "sandbox escapes in docker" or something.
gollark: Is it permitted to interfere with other entrants?
gollark: <@!293066066605768714> Is the program permitted to do arbitrary things to the machine on which it runs as long as they probably aren't bad much?
References
- "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- "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.
- "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- "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.
- "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.
- "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.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.