# 700 (number)

Short description: Natural number
 ← 699 700 701 →
Cardinalseven hundred
Ordinal700th
(seven hundredth)
Factorization22 × 52 × 7
Greek numeralΨ´
Roman numeralDCC
Binary10101111002
Ternary2212213
Quaternary223304
Quinary103005
Senary31246
Octal12748
Duodecimal4A412
Vigesimal1F020
Base 36JG36

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

It is the sum of four consecutive primes (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317)[1] and a Harshad number.

## 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 = prime number, sum of three consecutive primes (229 + 233 + 239), Chen prime, Eisenstein prime with no imaginary part
• 702 = 2 × 33 × 13, pronic number,[2] nontotient, Harshad number
• 703 = 19 × 37, triangular number,[3] hexagonal number,[4] smallest number requiring 73 fifth powers for Waring representation, Kaprekar number,[5] area code for Northern Virginia along with 571, a number commonly found in the formula for body mass index
• 704 = 26 × 11, Harshad number, lazy caterer number (sequence A000124 in the OEIS), area code for the Charlotte, NC area.
• 705 = 3 × 5 × 47, sphenic number, smallest Bruckman-Lucas pseudoprime (sequence A005845 in the OEIS)
• 706 = 2 × 353, nontotient, Smith number[6]
• 707 = 7 × 101, sum of five consecutive primes (131 + 137 + 139 + 149 + 151), palindromic number, number of lattice paths from (0,0) to (5,5) with steps (0,1), (1,0) and, when on the diagonal, (1,1).[7]
• 708 = 22 × 3 × 59, number of partitions of 28 that do not contain 1 as a part[8]
• 709 = prime number; 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 proceeding it in the series, therefore, it is a prime index number.

### 710s

• 710 = 2 × 5 × 71, sphenic number, nontotient, number of forests with 11 vertices [9][10]
• 711 = 32 × 79, Harshad number, number of planar Berge perfect graphs on 7 nodes.[11] Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.
• 712 = 23 × 89, refactorable number, 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, blum integer, 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, balanced number,[12] member of Ruth–Aaron pair (either definition); 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 = 5 × 11 × 13, sphenic number, pentagonal number,[13] pentatope number ( binomial coefficient $\displaystyle{ \tbinom {13}4 }$ ),[14] 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),[15] Sophie Germain prime,[16] safe prime,[17] sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part

### 720s

Main page: 720 (number)

### 730s

• 730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number, number of generalized weak orders on 5 points [30]
• 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251), number of Euler trees with total weight 7 [31]
• 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, number of collections of subsets of {1, 2, 3, 4} that are closed under union and intersection [32]
• 733 = prime number, emirp, balanced prime,[33] permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)
• 734 = 2 × 367, nontotient, number of traceable graphs on 7 nodes [34]
• 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,[35] happy number, nice Friedman number since 736 = 7 + 36, Harshad number
• 737 = 11 × 67, palindromic number, blum integer.
• 738 = 2 × 32 × 41, Harshad number.
• 739 = prime number, strictly non-palindromic number,[36] lucky prime,[25] happy number, prime index prime

### 740s

• 740 = 22 × 5 × 37, nontotient, number of connected squarefree graphs on 9 nodes [37]
• 741 = 3 × 13 × 19, sphenic number, triangular number[3]
• 742 = 2 × 7 × 53, sphenic number, decagonal number,[38] icosahedral number. It is the smallest number that is one more than triple its reverse. Lazy caterer number (sequence A000124 in the OEIS). Number of partitions of 30 into divisors of 30.[39]
Main page: 743 (number)
• 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 = 24 + 36, number of non-connected simple labeled graphs covering 6 vertices[40]
• 746 = 2 × 373 = 15 + 24 + 36 = 17 + 24 + 36, nontotient, number of non-normal semi-magic squares with sum of entries equal to 6[41]
• 747 = 32 × 83 = $\displaystyle{ \lfloor {\frac {4^{23}}{3^{23}}} \rfloor }$,[42] palindromic number.
• 748 = 22 × 11 × 17, nontotient, happy number, primitive abundant number[43]
• 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257), blum integer

### 750s

• 750 = 2 × 3 × 53, enneagonal number.[44]
• 751 = prime number, Chen prime, emirp
• 752 = 24 × 47, nontotient, number of partitions of 11 into parts of 2 kinds[45]
• 753 = 3 × 251, blum integer
• 754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers, number of different ways to divide a 10 × 10 square into sub-squares [46]
• 755 = 5 × 151, number of vertices in a regular drawing of the complete bipartite graph K9,9.[47]
• 756 = 22 × 33 × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number,[2] 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, prime number of measurement [48]
• 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163), a q-Fibonacci numbers for q=3 [49]

### 760s

• 760 = 23 × 5 × 19, centered triangular number,[50] number of fixed heptominoes.
• 761 = prime number, emirp, Sophie Germain prime,[16] Chen prime, Eisenstein prime with no imaginary part, centered square number[51]
• 762 = 2 × 3 × 127, sphenic number, sum of four consecutive primes (181 + 191 + 193 + 197), nontotient, Smith number,[6] admirable number, number of 1's in all partitions of 25 into odd parts,[52] see also Six nines in pi
• 763 = 7 × 109, sum of nine consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), number of degree-8 permutations of order exactly 2 [53]
• 764 = 22 × 191, telephone number[54]
• 765 = 32 × 5 × 17, octagonal pyramidal number [55]
• 766 = 2 × 383, centered pentagonal number,[56] nontotient, sum of twelve consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)
• 767 = 13 × 59, Thabit number (28 × 3 − 1), palindromic number.
• 768 = 28 × 3,[57] sum of eight consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109)
• 769 = prime number, Chen prime, lucky prime,[25] Proth prime[58]

### 770s

• 770 = 2 × 5 × 7 × 11, nontotient, Harshad number
• $\displaystyle{ \sum_{n=0}^{10} 770^{n} }$ is prime[59]
• 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 $\displaystyle{ \cos\left(\frac{2\pi}{771}\right) }$ can be written in terms of square roots.
• 772 = 22 × 193, 772!!!!!!+1 is prime[60]
• 773 = prime number, Eisenstein prime with no imaginary part, tetranacci number,[61] prime index prime
• 774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number
• 775 = 52 × 31, member of the Mian–Chowla sequence,[62] happy number
• 776 = 23 × 97, refactorable number, number of compositions of 6 whose parts equal to q can be of q2 kinds[63]
Main page: 777 (number)

### 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,[3] hexagonal number,[4] 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, lazy caterer number (sequence A000124 in the OEIS)
• 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,[13] Harshad number, also, 782 gear used by U.S. Marines
• 783 = 33 × 29, heptagonal number
• 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 positive integers, happy number
• 785 = 5 × 157, Mertens function(785) = 0, number of series-reduced planted trees with 6 leaves of 2 colors [67]
Main page: 786 (number)
• 786 = 2 × 3 × 131, sphenic number, admirable 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,[25] palindromic prime.
• 788 = 22 × 197, nontotient, number of compositions of 12 into parts with distinct multiplicities [68]
• 789 = 3 × 263, sum of three consecutive primes (257 + 263 + 269), blum integer

### 790s

Main page: 790 (number)
• 790 = 2 × 5 × 79, sphenic number, nontotient
• 791 = 7 × 113, centered tetrahedral number, 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,[69] binomial coefficient $\displaystyle{ \tbinom {12}5 }$, Harshad number, sum of the nontriangular numbers between successive triangular numbers
• 793 = 13 × 61, Mertens function(793) = 0, star number,[70] happy number
• 794 = 2 × 397 = 16 + 26 + 36,[71] nontotient
• 795 = 3 × 5 × 53, sphenic number, Mertens function(795) = 0, number of permutations of length 7 with 2 consecutive ascending pairs [72]
• 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, prime index prime.
• 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient, product of primes indexed by the prime exponents of 10! [73]
• 799 = 17 × 47, smallest number with digit sum 25 [74]

## References

1. Sloane, N. J. A., ed. "Sequence A024364 (Ordered perimeters of primitive Pythagorean triangles)". OEIS Foundation. Retrieved 2022-05-31.
2. "Sloane's A000217 : Triangular numbers". OEIS Foundation.
3. "Sloane's A000384 : Hexagonal numbers". OEIS Foundation.
4. "Sloane's A006886 : Kaprekar numbers". OEIS Foundation.
5. "Sloane's A006753 : Smith numbers". OEIS Foundation.
6. Sloane, N. J. A., ed. "Sequence A026671 (Number of lattice paths from (0,0) to (n,n) with steps (0,1), (1,0) and, when on the diagonal, (1,1))". OEIS Foundation. Retrieved 2022-05-22.
7. Sloane, N. J. A., ed. "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". OEIS Foundation. Retrieved 2022-06-02.
8. Hougardy, Stefan (6 October 2006). "Classes of perfect graphs - ScienceDirect". Discrete Mathematics. Creation and Recreation: A Tribute to the Memory of Claude Berge 306 (19): 2529–2571. doi:10.1016/j.disc.2006.05.021.
9. Sloane, N. J. A., ed. "Sequence A005195 (Number of forests with n unlabeled nodes)". OEIS Foundation. Retrieved 2022-05-22.
10. "Sloane's A000326 : Pentagonal numbers". OEIS Foundation.
11. "Sloane's A000332 : Binomial coefficient binomial(n,4)". OEIS Foundation.
12. "Sloane's A088054 : Factorial primes". OEIS Foundation.
13. "Sloane's A005384 : Sophie Germain primes". OEIS Foundation.
14. "Sloane's A005385 : Safe primes". OEIS Foundation.
15. "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation.
16. Sloane, N. J. A., ed. "Sequence A066897 (Total number of odd parts in all partitions of n)". OEIS Foundation. Retrieved 2022-05-22.
17. Sloane, N. J. A., ed. "Sequence A001105". OEIS Foundation.
18. Sloane, N. J. A., ed. "Sequence A016064 (Smallest side lengths of almost-equilateral Heronian triangles)". OEIS Foundation. Retrieved 2022-05-22.
19. Sloane, N. J. A., ed. "Sequence A003500". OEIS Foundation. Retrieved 2022-05-22.
20. Sloane, N. J. A., ed. "Sequence A335025 (Largest side lengths of almost-equilateral Heronian triangles)". OEIS Foundation. Retrieved 2022-05-22.
21. "Sloane's A002411 : Pentagonal pyramidal numbers". OEIS Foundation.
22. Sloane, N. J. A., ed. "Sequence A007749 (Numbers k such that k!! - 1 is prime)". OEIS Foundation. Retrieved 2022-05-24.
23. "Sloane's A082897 : Perfect totient numbers". OEIS Foundation.
24. Sloane, N. J. A., ed. "Sequence A004123 (Number of generalized weak orders on n points)". OEIS Foundation. Retrieved 2022-05-22.
25. Sloane, N. J. A., ed. "Sequence A007317 (Binomial transform of Catalan numbers)". OEIS Foundation.
26. Sloane, N. J. A., ed. "Sequence A306445 (Number of collections of subsets of {1, 2, ..., n} that are closed under union and intersection)". OEIS Foundation. Retrieved 2022-05-22.
27. "Sloane's A006562 : Balanced primes". OEIS Foundation.
28. Sloane, N. J. A., ed. "Sequence A057864 (Number of simple traceable graphs on n nodes)". OEIS Foundation. Retrieved 2022-05-22.
29. "Sloane's A069099 : Centered heptagonal numbers". OEIS Foundation.
30. "Sloane's A016038 : Strictly non-palindromic numbers". OEIS Foundation.
31. Sloane, N. J. A., ed. "Sequence A077269 (Number of connected squarefree graphs on n nodes)". OEIS Foundation. Retrieved 2022-05-23.
32. "Sloane's A001107 : 10-gonal (or decagonal) numbers". OEIS Foundation.
33. Sloane, N. J. A., ed. "Sequence A327070 (Number of non-connected simple labeled graphs covering n vertices)". OEIS Foundation. Retrieved 2022-05-23.
34. Sloane, N. J. A., ed. "Sequence A321719 (Number of non-normal semi-magic squares with sum of entries equal to n)". OEIS Foundation. Retrieved 2022-05-30.
35. Sloane, N. J. A., ed. "Sequence A064628 (Floor(4^n / 3^n))". OEIS Foundation. Retrieved 2022-05-30.
36. "Sloane's A091191 : Primitive abundant numbers". OEIS Foundation.
37. Sloane, N. J. A., ed. "Sequence A000712". OEIS Foundation. Retrieved 2022-05-30.
38. Sloane, N. J. A., ed. "Sequence A034295 (Number of different ways to divide an n X n square into sub-squares)". OEIS Foundation. Retrieved 2022-05-23.
39. Sloane, N. J. A., ed. "Sequence A331755 (Number of vertices in a regular drawing of the complete bipartite graph K_{9,9})". OEIS Foundation. Retrieved 2022-05-23.
40. Sloane, N. J. A., ed. "Sequence A002049 (Prime numbers of measurement)". OEIS Foundation. Retrieved 2022-05-23.
41. Sloane, N. J. A., ed. "Sequence A015474". OEIS Foundation. Retrieved 2022-05-23.
42. "Sloane's A005448 : Centered triangular numbers". OEIS Foundation.
43. "Sloane's A001844 : Centered square numbers". OEIS Foundation.
44. Sloane, N. J. A., ed. "Sequence A001189 (Number of degree-n permutations of order exactly 2)". OEIS Foundation. Retrieved 2022-05-23.
45. Sloane, N. J. A., ed. "Sequence A002414 (Octagonal pyramidal numbers)". OEIS Foundation. Retrieved 2022-05-23.
46. "Sloane's A005891 : Centered pentagonal numbers". OEIS Foundation.
47. Sloane, N. J. A., ed. "Sequence A007283". OEIS Foundation. Retrieved 2022-05-30.
48. "Sloane's A080076 : Proth primes". OEIS Foundation.
49. Sloane, N. J. A., ed. "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". OEIS Foundation. Retrieved 2022-05-30.
50. Sloane, N. J. A., ed. "Sequence A085150 (Numbers n such that n!!!!!!+1 is prime)". OEIS Foundation. Retrieved 2022-05-30.
51. "Sloane's A000078 : Tetranacci numbers". OEIS Foundation.
52. "Sloane's A005282 : Mian-Chowla sequence". OEIS Foundation.
53. (sequence A033453 in the OEIS)
54.
55. Dennis, Geoffrey. "Judaism & Numbers". My Jewish Learning.
56. "Sloane's A100827 : Highly cototient numbers". OEIS Foundation.
57. Sloane, N. J. A., ed. "Sequence A050381 (Number of series-reduced planted trees with n leaves of 2 colors)". OEIS Foundation. Retrieved 2022-05-24.
58. Sloane, N. J. A., ed. "Sequence A242882 (Number of compositions of n into parts with distinct multiplicities)". OEIS Foundation. Retrieved 2022-05-24.
59. "Sloane's A000041 : a(n) = number of partitions of n". OEIS Foundation.
60. Sloane, N. J. A., ed. "Sequence A001550". OEIS Foundation. Retrieved 2022-05-24.
61. Sloane, N. J. A., ed. "Sequence A000274 (Number of permutations of length n with 2 consecutive ascending pairs)". OEIS Foundation. Retrieved 2022-05-24.
62. Sloane, N. J. A., ed. "Sequence A325508 (Product of primes indexed by the prime exponents of n!)". OEIS Foundation. Retrieved 2022-05-24.
63. Sloane, N. J. A., ed. "Sequence A051885 (Smallest number whose sum of digits is n)". OEIS Foundation. Retrieved 2022-05-24.