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. In mathematics, a natural number is either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). The former definition is generally used in number theory, while the latter is preferred in set theory. ... 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 prime) is a natural number greater than one whose only positive divisors are one and itself. ...

We begin with a list of integers starting with 1: The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ...

 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: In mathematics, any integer (whole number) is either even or odd. ...

 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 

The second term in this sequence is 3. Now we cross out every third number which remains in the list: This is a page about mathematics. ...

 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: 7 (seven) is the natural number following 6 and preceding 8. ...

 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, ...

Stanisław Ulam was the first to discuss these numbers, around 1955. He named them "lucky" because of a connection with a story told by the historian Josephus. Look up one in Wiktionary, the free dictionary. ... 3 (three) is a number, numeral, and glyph. ... This article is about the number seven. ... 9 (nine) is the natural number following 8 and preceding 10. ... See also Thirteen, a 2003 movie, 13 an album by British band Blur, Thirteen an album by Teenage Fanclub. ... 15 (fifteen) is the natural number following 14 and preceding 16. ... 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 is the natural number following 32 and preceding 34. ... 37 is the natural number following 36 and preceding 38. ... 43 is the natural number following 42 and preceding 44. ... 49 is the natural number following 48 and preceding 50. ... 51 is the natural number following 50 and preceding 52. ... Sixty-three is a natural number following 62 and preceding 64. ... 67 is the natural number following 66 and preceding 68. ... 69 is the natural number following 68 and preceding 70. ... 73 is the natural number following 72 and preceding 74. ... 75 (seventy-five) is the natural number following 74 and preceding 76. ... 79 is the natural number following 78 and preceding 80. ... 87 is the natural number following 86 and preceding 88. ... 93 is the natural number following 92 and preceding 94. ... 99 (ninety-nine) is the natural number following 98 and preceding 100. ... StanisÅ‚aw Marcin Ulam (April 13, 1909–May 13, 1984) was a Polish mathematician who helped develop the key theory behind the hydrogen bomb. ... 1955 (MCMLV) was a common year starting on Saturday of the Gregorian calendar. ... Josephus (c. ...

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. There are infinitely many lucky numbers. It is not known whether there are also infinitely many lucky primes: In number theory, the prime number theorem (PNT) describes the approximate, asymptotic distribution of the prime numbers. ... In mathematics, Goldbachs conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. ... Headline text A lucky prime is a number that is a prime number and a lucky number. ...

3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, ...

External links

• Peterson, Ivars: MathTrek: Martin Gardner's Lucky Number: http://www.sciencenews.org/sn_arc97/9_6_97/mathland.htm
• Schneider, Walter: A list of the first 1000 lucky numbers: http://www.wschnei.de/number-theory/lucky-numbers-list.html
• Sloane, Neil J. A.: A sequence of lucky numbers - A000959: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=000959
• Sloane, Neil J. A.: A sequence of lucky primes - A031157: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=031157
• Sloane, Neil J. A.: A sequence of composite lucky numbers - A031879: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=031879
• Weisstein, Eric W.: Lucky Number: http://mathworld.wolfram.com/LuckyNumber.html
• Lucky Number Picker: http://www.banknotes.com/lottery.htm