# 700 (number)

(Redirected from 772 (number))
 ← 699 700 701 →
Cardinal seven hundred
Ordinal 700th
(seven hundredth)
Factorization 22× 52× 7
Greek numeral Ψ´
Roman numeral DCC
Binary 10101111002
Ternary 2212213
Quaternary 223304
Quinary 103005
Senary 31246
Octal 12748
Duodecimal 4A412
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:

## 700s

700 — see above

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

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.

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

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

720 (seven hundred [and] twenty)= 24 × 32 × 5.

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

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, 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

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, perhaps the most famous Boeing aircraft

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

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

750 (seven hundred [and] fifty)= 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

758 = 2 × 379, nontotient

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

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]

770 = 2 × 5 × 7 × 11, nontotient, Harshad number

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 ${\displaystyle \cos \left({\frac {2\pi }{771}}\right)}$ 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, 3333 in senary (base 6) counting.

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

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

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 = ${\displaystyle 1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}+7^{3}}$, the sum of the cubes of the first seven integers, happy number

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)

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 ${\displaystyle {\tbinom {12}{5}}}$, 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

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

799 = 17 × 47

## References

1. ^ 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.
2. ^ a b c "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
3. ^ a b "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.
5. "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
6. ^ a b "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
7. ^ "Sloane's A000332 : Binomial coefficient binomial(n,4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
8. ^ "Sloane's A088054 : Factorial primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
9. ^ a b "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
10. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
11. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
12. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
13. ^ 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.
14. ^ "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.
15. ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
16. ^ "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.
17. ^ "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
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19. ^ "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
20. ^ "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
21. ^ "Sloane's A091191 : Primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
22. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
23. ^ "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
24. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
25. ^ "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.
26. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
27. ^ "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
28. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
29. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
30. ^ Posner, Eliezer. "On the Meaning of Three". Chabad. Retrieved 2 July 2016.
31. ^ Dennis, Geoffrey. "Judaism & Numbers". My Jewish Learning. Retrieved 2 July 2016.
32. ^ "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
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34. ^ "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.