# 700 (number)

(Redirected from 756 (number))
 ← 699 700 701 →
Cardinalseven hundred
Ordinal700th
(seven hundredth)
Factorization22 × 52 × 7
Greek numeralΨ´
Roman numeralDCC
Binary10101111002
Ternary2212213
Octal12748
Duodecimal4A412

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

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

## Integers from 701 to 799

Nearly all of the palindromic integers between 700 and 800 are used as model numbers for Boeing Commercial Airplanes, and the only one not officially used by Boeing, 797, is commonly speculated to be the number of the next new Boeing commercial airplane.[1]

### 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,[7] pentatope number ( binomial coefficient ${\displaystyle {\tbinom {13}{4}}}$ ),[8]

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

### 740s

• 740 = 22 × 5 × 37, nontotient
• 741 = 3 × 13 × 19, sphenic number, triangular number[3]
• 742 = 2 × 7 × 53, sphenic number, decagonal number.[21] 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[22]
• 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257)

### 750s

• 750 = 2 × 3 × 53, enneagonal number.[23]
• 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,[2] Harshad number
• 757 = prime number, palindromic prime, sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127), happy number, model number for the Boeing 757
• 758 = 2 × 379, nontotient
• 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163)

### 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
• 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,[7] 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

### 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,[34] binomial coefficient ${\displaystyle {\tbinom {12}{5}}}$, Harshad number
• 793 = 13 × 61, Mertens function(793) = 0, star number,[35] 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, speculated model number for the Boeing New Midsize Airplane
• 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient
• 799 = 17 × 47

## References

1. ^ "The Boeing 797 - Here Are The Clues We Have So Far". Simple Flying. 2020-03-04. Retrieved 2021-04-06.
2. ^ 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.
3. ^ a b c "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
4. ^ a b "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
5. ^ "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
6. "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
7. ^ a b "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
8. ^ "Sloane's A000332 : Binomial coefficient binomial(n,4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
9. ^ "Sloane's A088054 : Factorial primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
10. ^ a b "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
11. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
12. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
13. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
14. ^ 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.
15. ^ "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.
16. ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
17. ^ "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.
18. ^ "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
19. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
20. ^ "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
21. ^ "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
22. ^ "Sloane's A091191 : Primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
23. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
24. ^ "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
25. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
26. ^ "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.
27. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
28. ^ "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
29. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
30. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
31. ^ Posner, Eliezer. "On the Meaning of Three". Chabad. Retrieved 2 July 2016.
32. ^ Dennis, Geoffrey. "Judaism & Numbers". My Jewish Learning. Retrieved 2 July 2016.
33. ^ "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
34. ^ "Sloane's A000041 : a(n) = number of partitions of n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
35. ^ "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.