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
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 preceding 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.
721 = 7 × 103, sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101),
centered hexagonal number,[18] smallest number that is the difference of two positive cubes in two ways,
722 = 2 × 192, nontotient, number of odd parts in all partitions of 15,[19] area of a square with diagonal 38[20]
G.722 is a freely available file format for audio file compression. The files are often named with the extension "722".
724 = 22 × 181, sum of four consecutive primes (173 + 179 + 181 + 191), sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137), nontotient, side length of an
almost-equilateral Heronian triangle,[22] the number of
n-queens problem solutions for n = 10,
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]
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]
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]
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]
773 = prime number, Eisenstein prime with no imaginary part,
tetranacci number,[61]prime index prime, sum of the number of cells that make up the convex, regular 4-polytopes
774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number
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
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 preceding 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.
721 = 7 × 103, sum of nine consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101),
centered hexagonal number,[18] smallest number that is the difference of two positive cubes in two ways,
722 = 2 × 192, nontotient, number of odd parts in all partitions of 15,[19] area of a square with diagonal 38[20]
G.722 is a freely available file format for audio file compression. The files are often named with the extension "722".
724 = 22 × 181, sum of four consecutive primes (173 + 179 + 181 + 191), sum of six consecutive primes (107 + 109 + 113 + 127 + 131 + 137), nontotient, side length of an
almost-equilateral Heronian triangle,[22] the number of
n-queens problem solutions for n = 10,
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]
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]
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]
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]
773 = prime number, Eisenstein prime with no imaginary part,
tetranacci number,[61]prime index prime, sum of the number of cells that make up the convex, regular 4-polytopes
774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number