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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).
These polynomials are all members of the larger set of prime generating polynomials. Leonhard Euler published the polynomial k 2 − 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). [1] Note that these numbers are all ...
All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
The number 13 is a prime number, happy number [2] and a lucky number. [3] It is a twin prime with 11, as well as a cousin prime with 17. It is the second of only 3 Wilson primes: 5, 13, and 563. A 13-sided regular polygon is called a tridecagon.
37 is the median value for the second prime factor of an integer. [5] Every positive integer is the sum of at most 37 fifth powers (see Waring's problem). [6] It is the third cuban prime following 7 and 19. [7] 37 is the fifth Padovan prime, after the first four prime numbers 2, 3, 5, and 7. [8] It is the fifth lucky prime, after 3, 7, 13, and ...
Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2 p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1.
the only safe primes that are also full reptend primes in base 12 are 5 and 7; q divides 3 (q−1)/2 − 1 and 12 (q−1)/2 − 1, same as 3 (q−1)/2 ≡ 1 mod q and 12 (q−1)/2 ≡ 1 mod q (per Euler's criterion) q-3, q-4, q-9, q-12 are quadratic nonresidues q-3, q-4, q-9, and, for q > 11, q-12 are primitive roots; If p is a Sophie Germain ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.