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Lucky number. In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers). [1]
These polynomials are all members of the larger set of prime generating polynomials. Leonhard Euler published the polynomial k2 − k + 41 which produces prime numbers for all integer values of k from 1 to 40. Only 6 lucky numbers of Euler exist, namely 2, 3, 5, 11, 17 and 41 (sequence A014556 in the OEIS ). Note that these numbers are all ...
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
A -happy prime is a number that is both -happy and prime. Unlike happy numbers, rearranging the digits of a -happy prime will not necessarily create another happy prime. For instance, while 19 is a 10-happy prime, 91 = 13 × 7 is not prime (but is still 10-happy). All prime numbers are 2-happy and 4-happy primes, as base 2 and base 4 are happy ...
All prime numbers are known to be solitary, as are powers of prime numbers. More generally, if the numbers n and σ( n ) are coprime – meaning that the greatest common divisor of these numbers is 1, so that σ( n )/ n is an irreducible fraction – then the number n is solitary (sequence A014567 in the OEIS ).
37 is the fifth Padovan prime, after the first four prime numbers 2, 3, 5, and 7. It is the fifth lucky prime, after 3, 7, 13, and 31. 37 is a sexy prime, being 6 more than 31, and 6 less than 43. 37 remains prime when its digits are reversed, thus it is also a permutable prime.
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1987 is an odd number and the 300th prime number.It is the first number of a sexy prime triplet (1987, 1993, 1999). Being of the form 4n + 3, it is a Gaussian prime.It is a lucky number and therefore also a lucky prime. 1987 is a prime factor of the 9th number in Sylvester's sequence, and is the 15th prime to divide any number in the sequence.
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