In number theory, a lucky number is a natural number in a set which is generated by a "sieve" similar to the Sieve of Eratosthenes that generates the primes. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an Sieve theory is a set of general techniques in Number theory, designed to count or more realistically to estimate the size of sifted sets of integers In Mathematics, the Sieve of Eratosthenes is a simple ancient Algorithm for finding all Prime numbers up to a specified integer In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1
We begin with a list of integers starting with 1:
1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
Then we cross out every second number (all even numbers), leaving only the odd integers:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25,
The second term in this sequence is 3. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French In Mathematics, the parity of an object states whether it is even or odd In Mathematics, a sequence is an ordered list of objects (or events Now we cross out every third number which remains in the list:
1, 3, 7, 9, 13, 15, 19, 21, 25,
The third surviving number is now 7 so we cross out every seventh number that remains:
1, 3, 7, 9, 13, 15, 21, 25,
If we repeat this procedure indefinitely, the survivors are the lucky numbers:
- 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, . Mathematics For any number x: x ·1 = 1· x = x (1 is the multiplicative identity ---- In mathematics Three is the first odd Prime number, and the second smallest prime In mathematics Seven is the fourth Prime number. It is not only a Mersenne prime (since 23 &minus 1 = 7 but also a In mathematics Nine is a Composite number, its proper Divisors being 1 and 3. 21 ( twenty-one) is the Natural number following 20 and preceding 22. 25 ( twenty-five) is the Natural number following 24 and preceding 26. 31 ( thirty-one) is the Natural number following 30 and preceding 32. 33 ( thirty-three) is the Natural number following 32 and preceding 34. 37 ( thirty-seven) is the Natural number following 36 and preceding 38. 43 ( forty-three) is the Natural number following 42 and preceding 44. This page is for the number For the steamboat see Forty-Nine (steamboat 49 ( forty-nine) is the Natural number following 48 51 ( fifty-one) is the Natural number 51 following 50 and preceding 52. 63 ( sixty-three) is a Natural number following 62 and preceding 64. 67 ( sixty-seven) is the Natural number following 66 and preceding 68. 69 ( sixty-nine) is a number following 68 and preceding 70. In mathematics sixty-nine is the twentieth distinct Biprime 73 ( seventy-three) is the Natural number following 72 and preceding 74. 75 ( seventy-five) is the Natural number following 74 and preceding 76. 79 ( seventy-nine) is the Natural number following 78 and preceding 80. 87 ( eighty-seven) is the Natural number following 86 and preceding 88. 93 ( ninety-three) is the Natural number following 92 and preceding 94. 99 ( ninety-nine) is the Natural number following 98 and preceding 100. . . (sequence A000959 in OEIS). The On-Line Encyclopedia of Integer Sequences ( OEIS) also cited simply as Sloane's, is an extensive searchable Database of Integer sequences
The term was introduced in 1955 in a paper by Gardiner, Lazarus, Metropolis and Ulam. They suggest also calling its defining sieve the sieve of Josephus Flavius. Josephus (AD 37 – c 100 also known as Yosef Ben Matityahu (Joseph son of Matthias and after he became a Roman citizen, as Titus Flavius Josephus [1]
Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also Goldbach's conjecture has been extended to them. Goldbach's conjecture is one of the oldest unsolved problems in Number theory and in all of Mathematics. There are infinitely many lucky numbers. Because of these apparent connections with the prime numbers, some mathematicians have suggested that these properties may be found in a larger class of sets of numbers generated by sieves of a certain unknown form, although there is little theoretical basis for this conjecture. In Mathematics, a conjecture is a Mathematical statement which appears resourceful but has not been formally proven to be true under the rules of Twin lucky numbers and twin primes also appear to occur with similar frequency. A twin prime is a Prime number that differs from another prime number by Two.
A lucky prime is a lucky number that is prime. It is not known whether there are infinitely many lucky primes. The first few are
- 3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193 (sequence A031157 in OEIS). The On-Line Encyclopedia of Integer Sequences ( OEIS) also cited simply as Sloane's, is an extensive searchable Database of Integer sequences
See also
External links
- Peterson, Ivars. A Fortunate number, named after Reo Fortune, for a given positive Integer n is the smallest integer m > 1 such that p n MathTrek: Martin Gardner's Lucky Number
- Eric W. Weisstein, Lucky Number at MathWorld. Eric W Weisstein (born March 18, 1969, in Bloomington Indiana) is an Encyclopedist who created and maintains MathWorld MathWorld is an online Mathematics reference work created and largely written by Eric W
- Lucky Numbers by Enrique Zeleny, The Wolfram Demonstrations Project.
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