"prime factor of the Euclid number 510511 = 2 × 3 × 5 × 7 × 11 × 13 × 17 + 1. As a member of the lazy caterer's sequence, 277 counts the maximum number of pieces obtained by slicing a pancake with 23 straight cuts. 277 is also a Perrin number, and as such counts the number of maximal independent sets in an icosagon. There are 277 ways to tile a 3 × 8 rectangle with integer-sided squares, and 277 degree-7 monic polynomials with integer coefficients and all roots in the unit disk. On an infinite chessboard, there"
"the Bábí and Bahá'í faiths, a group of 19 is called a ""Váhid"", a Unity (Arabic: واحد ""wāhid"", ""one""). The numerical value of this word in the Abjad numeral system is 19. 19 (number) 19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number. In English speech, the numbers 19 and 90 are sometimes confused, as they sound very similar. 19 is the 8th prime number. 19 is the seventh Mersenne prime exponent. 19 is the maximum number of fourth powers needed to sum up to any natural number. It is the fourth value"
"Fibonacci numbers satisfies the recurrence with initial conditions Explicitly, the recurrence yields the values etc. The sequence 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, ... of Lucas numbers satisfies the same recurrence as the Fibonacci sequence but with initial conditions More generally, every Lucas sequence is a constant-recursive sequence. The geometric sequence formula_16 is constant-recursive, since it satisfies the recurrence formula_17 for all formula_18. A sequence that is eventually periodic with period length formula_19 is constant-recursive, since it satisfies formula_20 for all formula_4 for some ""d"". For any polynomial ""s""(""n""), the sequence of its values"
"111 (number) 111 (One hundred [and] eleven) is the natural number following 110 and preceding 112. 111 is a perfect totient number. 111 is R or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 × 37, therefore all triplets (numbers like 222 or 777) in base ten are of the form 3""n"" × 37. As a repunit, it also follows that 111 is a palindromic number. All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base"
"+ 31 + 37 + 41 + 43 + 47) 319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number, cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10 ""319"" is a song by Prince. British Rail Class 319s are dual-voltage electric multiple unit trains 320 = 2 × 5 = (2) × (2 × 5). 320 is a Leyland number, maximum determinant of a 10 by 10 matrix of zeros and ones, and a Harshad number. A popular bitrate. 321 ="
"another example, if ""n"" = 2, then 10""n"" − 1 = 19 and the repeating decimal for 1/19 is So that for 2/19 is double that: The length ""m"" of this period is 18, the same as the order of 10 modulo 19, so = 105263157894736842. 105263157894736842 × 2 = 210526315789473684, which is the result of moving the last digit of 105263157894736842 to the front. The smallest ""n""-parasitic numbers are also known as Dyson numbers, after a puzzle concerning these numbers posed by Freeman Dyson. They are: (leading zeros are not allowed) In general, if we relax the rules to"
"Hilbert number In number theory, a branch of mathematics, a Hilbert number is a positive integer of the form (). The Hilbert numbers were named after David Hilbert. The sequence of Hilbert numbers begins 1, 5, 9, 13, 17, ... ). A Hilbert prime is a Hilbert number that is not divisible by a smaller Hilbert number (other than 1). The sequence of Hilbert primes begins A Hilbert prime is not necessarily a prime number; for example, 21 is a composite number since . However, 21 a Hilbert prime since neither 3 nor 7 (the only factors of 21 other"
"17 (number) 17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. In English speech, the numbers 17 and 70 are sometimes confused, as they sound very similar. The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena. Seventeen is the sum of the first four prime numbers. Seventeen is the seventh prime number. The next prime is nineteen, with which it forms a twin prime. Seventeen is a permutable prime and a supersingular prime. Seventeen is the third Fermat prime,"
"but 1 and themselves. Taking these in their natural order gives the sequence (2, 3, 5, 7, 11, 13, 17, ...). The prime numbers are widely used in mathematics and specifically in number theory. The Fibonacci numbers are the integer sequence whose elements are the sum of the previous two elements. The first two elements are either 0 and 1 or 1 and 1 so that the sequence is (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...). For a large list of examples of integer sequences, see On-Line Encyclopedia of Integer Sequences. Other examples of sequences include"
"the first 29 natural numbers have more than two different prime factors. This is the longest such consecutive sequence. 29 is a Markov number, appearing in the solutions to ""x"" + ""y"" + ""z"" = 3""xyz"": {2, 5, 29}, {2, 29, 169}, {5, 29, 433}, {29, 169, 14701}, etc. 29 is a Perrin number, preceded in the sequence by 12, 17, 22. 29 is the smallest positive whole number that cannot be made from the numbers {1, 2, 3, 4}, using each exactly once and using only addition, subtraction, multiplication, and division. 29 (number) 29 (twenty-nine) is the natural number"
"the only prime number which is the sum of four consecutive primes (2,3,5,7). Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime. In Catalan, 17 is the first compound number (""disset""). The numbers 11 (""onze"") through 16 (""setze"") have their own names. In French, 17 is the first compound number (""dix-sept""). The numbers 11 (""onze"") through 16 (""seize"") have their own names. In Italian, 17 is also the first compound number (""diciassette""), whereas sixteen is ""sedici"". Seventeen is: 17 (number) 17 (seventeen) is the natural number following 16 and"
"Zeisel number A Zeisel number, named after Helmut Zeisel, is a square-free integer ""k"" with at least three prime factors which fall into the pattern where ""a"" and ""b"" are some integer constants and ""x"" is the index number of each prime factor in the factorization, sorted from lowest to highest. For the purpose of determining Zeisel numbers, formula_2. The first few Zeisel numbers are To give an example, 1729 is a Zeisel number with the constants ""a"" = 1 and ""b"" = 6, its factors being 7, 13 and 19, falling into the pattern 1729 is an example for"
"""2"" and ""3"", and with a base number (subscripted) ""8"", means 19. In our notation here, the subscript """" of the numeral 23 is part of the numeral, but this may not always be the case. Imagine the numeral ""23"" as having an ambiguous base number. Then ""23"" could likely be any base, base-4 through base-60. In base-4 ""23"" means 11, and in base-60 it means the number 123. The numeral ""23"" then, in this case, corresponds to the set of numbers {11, 13, 15, 17, 19, 21, 23, ..., 121, 123} while its digits ""2"" and ""3"" always retain"
"2, 4 and 7, corresponding to the Thabit primes 11, 47 and 383 given by ""n"", the Thabit primes 5, 23 and 191 given by ""n""−1, and our third terms are 71, 1151 and 73727. (The corresponding amicable pairs are (220, 284), (17296, 18416) and (9363584, 9437056)) For integer ""b"" ≥ 2, a Thabit number base ""b is a number of the form (""b""+1)·""b"" − 1 for a non-negative integer ""n"". Also, for integer ""b"" ≥ 2, a Thabit number of the second kind base ""b is a number of the form (""b""+1)·""b"" + 1 for a non-negative integer ""n""."
"of ""U""'s is : ""U"" = 0, ""U"" = 1, ""U"" = 3, ""U"" = 10, etc. First, let ""n"" = 19. The Jacobi symbol formula_7 is −1, so δ(""n"") = 20, ""U"" = 6616217487 = 19·348221973 and we have Therefore, 19 is a Lucas probable prime for this (""P, Q"") pair. In this case 19 is prime, so it is ""not"" a Lucas pseudoprime. For the next example, let ""n"" = 119. We have formula_9 = −1, and we can compute However, 119 = 7·17 is not prime, so 119 is a Lucas ""pseudoprime"" for this (""P, Q"") pair."
"a numeral system of their own, based on powers of 4. The base numerals are one (1), two (2), three (3), many (4) and lots (16), which can be combined to form higher numbers. When combined, each numeral's value is added to those of the others. Higher-valued numerals take priority over lower-valued ones, so that 4 is written ""many"" and not ""two-two"" or ""three-one"" and 20 is written ""lots many"" rather than ""many many many many many"". If there are no ones, twos or threes, the number is written with spaces between the numerals; if any exist a hyphen replaces"
"311 (number) 311 (three hundred [and] eleven) is the natural number following 310 and preceding 312. 311 is the 64th prime; a twin prime with 313; an irregular prime; an Eisenstein prime with no imaginary part and real part of the form formula_1; a Gaussian prime with no imaginary part and real part of the form formula_2; and a permutable prime with 113 and 131. It can be expressed as a sum of consecutive primes in four different ways: as a sum of three consecutive primes (101 + 103 + 107), as a sum of five consecutive primes (53 +"
"6, 7, 8, 8, 10, 13, 15, 16, 20} are {7, 9, 15}. If also required, the zeroth quartile is 3 and the fourth quartile is 20. Consider an ordered population of 11 data values {3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20}. What are the 4-quantiles (the ""quartiles"") of this dataset? So the first, second and third 4-quantiles (the ""quartiles"") of the dataset {3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20} are {7, 9, 15}. If also required, the zeroth quartile is 3 and the fourth quartile is 20. When one has a"
"18. Adding 19, however, gives 510529, which is prime. Hence 19 is a Fortunate number. The Fortunate number for ""p""# is always above ""p"" and all its divisors are larger than ""p"". This is because ""p""#, and thus ""p""# + ""m"", is divisible by the prime factors of ""m"" not larger than ""p"". The Fortunate numbers for the first primorials are: The Fortunate numbers sorted in numerical order with duplicates removed: Reo Fortune conjectured that no Fortunate number is composite (""Fortune's conjecture""). A Fortunate prime is a Fortunate number which is also a prime number. , all the known Fortunate"
"is 1, 7, 21, 107, 273, 1911, 5189, 28123, ... . This can be obtained by taking the coefficients of the successive powers of (1+""x""+""x"") modulo 2 and interpreting them as integers in binary. The sequence generated is 1, 7, 29, 115, 477, 1843, 7645, 29491, ... . This has generating function The sequence generated is 1, 3, 5, 15, 29, 55, 93, 247, ... . This has generating function The sequence generated is 1, 7, 29, 119, 477, 1911, 7645, 30583, ... . This has generating function The sequence generated is 1, 3, 7, 15, 31, 63, 127, 255,"
"Blum integer. 133 is also: 133 (number) 133 (one hundred [and] thirty-three) is the natural number following 132 and preceding 134. 133 is an ""n"" whose divisors (excluding ""n"" itself) added up divide φ(""n""). It is an octagonal number and a Harshad number. It is also a happy number. 133 is a repdigit in base 11 (111) and base 18 (77), whilst in base 20 it is a cyclic number formed from the reciprocal of the number three. 133 is a semiprime: a product of two prime numbers, namely 7 and 19. Since those prime factors are Gaussian primes, this"
"""n"" for ""k"" > 4 (and ""n"" > 1). Palindromic numbers can be considered in numeral systems other than decimal. For example, the binary palindromic numbers are: or in decimal: 0, 1, 3, 5, 7, 9, 15, 17, 21, 27, 31, 33, … . The Fermat primes and the Mersenne primes form a subset of the binary palindromic primes. All numbers are palindromic in an infinite number of bases. But, it's more interesting to consider bases smaller than the number itself - in which case most numbers are palindromic in more than one base, for example, formula_2, formula_3 In base"
"types of palindromic numbers these values are listed below in a table. Here 0 is included. There are many palindromic perfect powers ""n"", where ""n"" is a natural number and ""k"" is 2, 3 or 4. The first nine terms of the sequence 1, 11, 111, 1111, ... form the palindromes 1, 121, 12321, 1234321, ... The only known non-palindromic number whose cube is a palindrome is 2201, and it is a conjecture the fourth root of all the palindrome fourth powers are a palindrome with 100000...000001 (10 + 1). G. J. Simmons conjectured there are no palindromes of form"
"all words for cardinal numbers are necessarily numerals. For example, ""million"" is grammatically a noun, and must be preceded by an article or numeral itself. Numerals may be simple, such as 'eleven', or compound, such as 'twenty-three'. In linguistics, however, numerals are classified according to purpose: examples are ordinal numbers (""first"", ""second"", ""third"", etc.; from 'third' up, these are also used for fractions), multiplicative numbers (""once"", ""twice"", and ""thrice""), multipliers (""single"", ""double"", and ""triple""), and distributive numbers (""singly"", ""doubly"", and ""triply""). Georgian, Latin, and Romanian (see Romanian distributive numbers) have regular distributive numbers, such as Latin ""singuli"" ""one-by-one"", ""bini"" ""in"
"211 (number) 211 (two hundred [and] eleven) is the natural number between 210 and 212. It is also a prime number. 211 is an odd number. 211 is a primorial prime, sum of three consecutive primes (67 + 71 + 73), Chen prime, centered decagonal prime, and self prime. 211 is a repdigit in base 14 (111). Multiplying its digits, it is still a prime (2), and adding its digits, it is square (4). Rearranging its digits, 211 becomes 121, which also is a square. Adding any two of its digits will be prime (2 or 3). 2-1-1 is special"
"179 (number) 179 (one hundred [and] seventy-nine) is the natural number following 178 and preceding 180. 179 is an odd number. 179 is a prime number; that is, it is not divisible by integer (except for 1 and itself). It is an Eisenstein prime, as it is indivisible even by complex Gaussian integers. It is a Chen prime, being two less than another prime, 181. It is a full reptend prime, meaning 1/179 has a decimal expansion of a repeated sequence of 178 digits. 179 is a safe prime, as it is one more than two times the prime 89."
"than 1 and itself) are Hilbert numbers. It follows from multiplication modulo 4 that a Hilbert prime is either a prime number of the form (called a Pythagorean prime), or a semiprime of the form . Hilbert number In number theory, a branch of mathematics, a Hilbert number is a positive integer of the form (). The Hilbert numbers were named after David Hilbert. The sequence of Hilbert numbers begins 1, 5, 9, 13, 17, ... ). A Hilbert prime is a Hilbert number that is not divisible by a smaller Hilbert number (other than 1). The sequence of Hilbert"
"and can flipped back to front, flipped front to back, mirrored up-down, or flipped up-down and always stay the same. The four-way symmetry explains the name, due to tetra- being the Greek prefix for four. Tetradic numbers are both strobogrammatic and palindromic. If you have a tetradic number, a larger one can always be generated by adding another tetradic number to each end, retaining the symmetry. Tetradic primes are a specific type of tetradic number defined as tetradic numbers that are also prime numbers. The first few tetradic primes are 11, 101, 181, 18181, 1008001, 1180811, 1880881, 1881881, ... (OEIS"
"thus all ""E""+1 have a final digit of 1. It is not known whether there is an infinite number of prime Euclid numbers (primorial primes). It is also unknown whether every Euclid number is a squarefree number. A Euclid number of the second kind (also called Kummer number) is an integer of the form ""E"" = ""p""# − 1, where ""p#"" is the nth primorial. The first few such numbers are: As with the Euclid numbers, it is not known whether there are infinitely many prime Kummer numbers. The first of these numbers to be composite is 209. Euclid number"
"59 + 61 + 67 + 71), as a sum of seven consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59), and as a sum of eleven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). 311 is a strictly non-palindromic number, as it is not palindromic in any base between base 2 and base 309. 311 is the smallest positive integer ""d"" such that the imaginary quadratic field Q() has class number = 19. 311 (number) 311 (three hundred"
"fall into three classes: Thus, inert primes are 3, 7, 11, 19, ... and a factorization of the split primes is The associates and conjugate of a prime are also primes. Note that the norm of an inert prime ""q"" is N""q"" = ""q"" ≡ 1 (mod 4); thus the norm of all primes other than 1 + ""i"" and its associates is ≡ 1 (mod 4). Gauss calls a number in Z[""i""] odd if its norm is an odd integer. Thus all primes except 1 + ""i"" and its associates are odd. The product of two odd numbers is"
"720 (number) 720 (seven hundred [and] twenty) 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. 720 is expressible as the product of consecutive integers in two different ways: , and . There are 49 solutions to the equation φ(""x"") = 720, more than any integer below it, making 720 a highly totient number. 720 is a 241-gonal number. 720 is: For the year AD, see"
"two and three for ten and eleven, respectively) For base 2 self numbers, see . (written in base 10) The following table was calculated in 2007. Self number A self number, Colombian number or Devlali number is an integer that cannot be written as the sum of any other integer ""n"" and the individual digits of ""n"". This property is specific to the base used to represent the integers. 20 is a self number (in base 10), because no such combination can be found (all ""n"" < 15 give a result < 20; all other ""n"" give a result >"