ⓘ Free online encyclopedia. Did you know? page 118

511 (number)

511 is the natural number following 510 and preceding 512. It is a Mersenne number, being one less than a power of 2: 511 = 2 9 − 1 {\displaystyle 511=2^{9}-1}. As a result, 511 is a palindromic number and a repdigit in bases 2 111111111 2. It is ...

512 (number)

512 is the natural number following 511 and preceding 513. 512 is a power of two: 2 9 2 to the 9th power and the cube of 8: 8 3. It is the eleventh Leyland number. 512 is also the third Dudeney number.

52 (number)

Fifty-two is the 6th Bell number and a decagonal number. It is an untouchable number, since it is never the sum of proper divisors of any number, and it is a noncototient since it is never the answer to the equation x − φx.

53 (number)

53 written in hexadecimal is 35, that is, the same characters used in the decimal representation, but reversed. Four additional multiples of 53 share this property: 371 = 173 16, 5141 = 1415 16, 99481 = 18499 16, and 8520280 = 0820258 16. Apart f ...

54 (number)

54 is a 19-gonal number. Twice the third power of three, 54 is a Leyland number. 54 can be written as the sum of three squares in three different ways: 7 2 + 2 + 1 2 = 6 2 + 3 2 + 3 2 = 5 2 + 5 2 + 2 = 54. It is the smallest number with this prop ...

55 (number)

55 is the 10th Fibonacci number and a triangular number the sum of the consecutive numbers 1 to 10. It is the largest Fibonacci number to also be a triangular number. It is a square pyramidal number the sum of the squares of the integers 1 to 5 a ...

555 (number)

It is a sphenic number. In base 10, it is a repdigit, and because it is divisible by the sum of its digits, it is a Harshad number. It is also a Harshad number in binary, base 11, base 13 and hexadecimal.

56 (number)

56 is: the sum of the first six triangular numbers making it a tetrahedral number a tetranacci number and a pronic number the sum of the sums of the divisors of the first 8 positive integers a semiperfect number, since 56 is twice a perfect numbe ...

57 (number)

Fifty-seven is the sixteenth discrete semiprime and the sixth in the 3.q family. With 58 it forms the fourth discrete bi-prime pair. 57 has an aliquot sum of 23 and is the first composite member of the 23-aliquot tree. Although 57 is not prime, i ...

58 (number)

Fifty-eight is the sum of the first seven prime numbers, an 11-gonal number, and a Smith number. Given 58, the Mertens function returns 0. There is no solution to the equation x – φx = 58, making 58 a noncototient. However, the sum of the totient ...

59 (number)

Fifty-nine is the 17th prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary part and real part of the form ...

593 (number)

593 is an odd number. It is a prime number, an example of what Paul Erdos and Ernst G. Straus called a Good prime, or a prime whose square is greater than the product of its neighboring two primes. As such it is part of sequence A028388 at the On ...

6

6 is the smallest positive integer which is neither a square number nor a prime number. Six is the second smallest composite number; its proper divisors are 1, 2 and 3. Since six equals the sum of its proper divisors, six is the smallest perfect ...

60 (number)

It is a composite number, with divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, making it a highly composite number. Because it is the sum of its unitary divisors excluding itself, it is a unitary perfect number, and it is an abundant numbe ...

600 (number)

In the United States, a credit score of 600 or below is considered a poor score, thus limiting available credit or requiring the borrower to pay higher interest rates. In Latin, sescenti often denoted a very large but indefinite number, perhaps f ...

61 (number)

61 is: the sixth Euler zigzag number or Up/down number. a twin prime with 59. a centered hexagonal number. the sum of two squares, 5 2 + 6 2. palindromic in bases 6 141 6 and 60 11 60 a centered square number. a unique prime in base 14, since no ...

613 (number)

613 is a prime number, the first number of prime triplet, middle number of sexy prime triple p − 6, p, p + 6. It is the index of a prime Lucas number. 613 is a centered square number with 18 per side, a circular number of 21 with a square grid an ...

6174 (number)

6174 is known as Kaprekars constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following rule: Take any four-digit number, using at least two different digits. Leading zeros are allowed. Subtract the smaller num ...

62 (number)

62 is: the tenth member of the 7-aliquot tree 7, 8, 10, 14, 20, 22, 34, 38, 49, 62, 75, 118, 148, etc. It has an aliquot sum of 34; itself a discrete semiprime, and its aliquot sequence is: 62.34.20.22.14.10.8.7.1.0. a nontotient. palindromic and ...

63 (number)

63 is: the smallest whole number that can be divided by any number from 1 to 9 without repeating decimals. a Woodall number i.e. of the form 2 n − 1 with n = 4. a highly cototient number. the third Delannoy number. palindromic and a repdigit in b ...

64 (number)

Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum o ...

65 (number)

Sixty-five is the 23rd semiprime and the 3rd of the form 5.q. It is an octagonal number. It is also a Cullen number. Given 65, the Mertens function returns 0. This number is the magic constant of 5 by 5 normal magic square: . {\displaystyle {\beg ...

65.536

65536 is the natural number following 65535 and preceding 65537. 65536 is a power of two: 2 16 {\displaystyle 2^{16}} 2 to the 16th power. 65536 is the smallest number with exactly 17 divisors.

65.537

65537 is the largest known prime number of the form 2 n + 1 {\displaystyle 2^{2^{n}}+1} n = 4 {\displaystyle n=4}. Therefore, a regular polygon with 65537 sides is constructible with compass and unmarked straightedge. Johann Gustav Hermes gave th ...

66 (number)

66 is: palindromic and a repdigit in bases 10 66 10, 21 33 21 and 32 22 32 a hexagonal number. a semiperfect number, being a multiple of a perfect number. an Erdos–Woods number, since it is possible to find sequences of 66 consecutive integers su ...

666 (number)

666 is the natural number following 665 and preceding 667. 666 is called the "number of the Beast" in most manuscripts of chapter 13 of the Book of Revelation, of the New Testament, and also in popular culture.

67 (number)

67 is: the 19th prime number the next is 71. a lucky prime. a Heegner number. an irregular prime. palindromic in the consecutive bases 5 232 5 and 6 151 6. a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of ...

68 (number)

68 is a Perrin number. It is the largest known number to be the sum of two primes in exactly two different ways: 68 = 7 + 61 = 31 + 37. All higher even numbers that have been checked are the sum of three or more pairs of primes; the conjecture th ...

69 (number)

69 is: the third composite number in the 13-aliquot tree. The aliquot sum of sixty-nine is 27 within the aliquot sequence 69.27.13.1.0. the sum of the sums of the divisors of the first 9 positive integers. a lucky number. a semiprime. a Blum inte ...

E (mathematical constant)

The number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828, and is the limit of n as n approaches infinity, an expression that ...

Pi

The number π is a mathematical constant. Originally defined as the ratio of a circles circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximate ...

−1

In mathematics, −1 is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two and less than 0. Negative one bears relation to Eulers identity ...

7

In the beginning, various Hindus wrote 7 more or less in one stroke as a curve that looks like an uppercase J vertically inverted. The western Ghubar Arabs main contribution was to make the longer line diagonal rather than straight, though they s ...

70 (number)

70 is: the seventh pentagonal number. the fifth pentatope number. an Erdos–Woods number, since it is possible to find sequences of 70 consecutive integers such that each inner member shares a factor with either the first or the last member. the s ...

71 (number)

71 is: the algebraic degree of Conways constant, a remarkable number arising in the study of look-and-say sequences. the smallest positive integer d such that the imaginary quadratic field Q √ – d has class number = 7. part of the last known pair ...

72 (number)

Seventy-two is the sum of four consecutive primes 13 + 17 + 19 + 23, as well as the sum of six consecutive primes 5 + 7 + 11 + 13 + 17 + 19. The product of 8 and 9, 72 is a pronic number. The sum of Eulers totient function φx over the first fifte ...

720 (number)

720 is the natural number following 719 and preceding 721. It is 6! 6 factorial, a composite number with thirty divisors, more than any number below, making it a highly composite number. It is a Harshad number in every base from binary to decimal ...

73 (number)

73 is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

700 (number)

700 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.

74 (number)

74 is: a nontotient. the twenty-first distinct semiprime and the eleventh of the form 2× q. a palindromic number in bases 6 202 6 and 36 22 36. There are 74 different non-Hamiltonian polyhedra with a minimum number of vertices.

743 (number)

743 is the natural number following 742 and preceding 744. It is a prime number. 743 is a Sophie Germain prime, because 2 × 743 + 1 = 1487 is also prime. There are exactly 743 independent sets in a four-dimensional 16 vertex hypercube graph, and ...

76 (number)

76 is: a nontotient. a telephone number. a Lucas number. a 14-gonal number. a centered pentagonal number. One of two 2-digit numbers whose square, and higher powers, end in the same two digits. The other is 25. an Erdos–Woods number since it is p ...

77 (number)

77 is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.

78 (number)

78 is: a Harshad number in bases 3, 4, 5, 6, 7, 13 and 14. an Erdos–Woods number, since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member. a sphenic nu ...

79 (number)

79 is: A permutable prime, with ninety-seven. The smallest number that can not be represented as a sum of fewer than 19 fourth powers. The 22nd prime number between 73 and 83 A prime number that is also a Gaussian prime since it is of the form 4 ...

8

8 is: the only nonzero perfect power that is one less than another perfect power, by Mihailescus Theorem. a composite number, its proper divisors being 1, 2, and 4. It is twice 4 or four times 2. the base of the octal number system, which is most ...

80 (number)

80 is: a semiperfect number, since adding up some subsets of its divisors e.g., 1, 4, 5, 10, 20 and 40 gives 80. a menage number. palindromic in bases 3 2222 3, 6 212 6, 9 88 9, 15 55 15, 19 44 19 and 39 22 39. a repdigit in bases 3, 9, 15, 19 an ...

800 (number)

800 is the natural number following 799 and preceding 801. It is the sum of four consecutive primes 193 + 197 + 199 + 211. It is a Harshad number.

801 (number)

801 is the natural number following 800 and preceding 802. 801 is the sum of a square and positive cube in more than one way, and a sum of distinct positive cubes in more than one way: 801 = 17 2 + 8 3 = 26 2 + 5 3 = 1 3 + 2 3 + 4 3 + 6 3 + 8 3 = ...

81 (number)

81 is: the square of 9 and the fourth power of 3. a palindromic number in bases 8 121 8 and 26 33 26. the ninth member of the Mian-Chowla sequence. a Harshad number in bases 2, 3, 4, 7, 9, 10 and 13. a heptagonal number. one of three non-trivial ...

Free and no ads
no need to download or install

Pino - logical board game which is based on tactics and strategy. In general this is a remix of chess, checkers and corners. The game develops imagination, concentration, teaches how to solve tasks, plan their own actions and of course to think logically. It does not matter how much pieces you have, the main thing is how they are placement!

online intellectual game →