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There are infinitely many lucky numbers. Twin lucky numbers and twin primes also appear to occur with similar frequency. However, if L n denotes the n-th lucky number, and p n the n-th prime, then L n > p n for all sufficiently large n. [3]
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.
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.
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 ...
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a Proth prime as it is 5 × 2 3 + 1. [3] the largest lucky number of Euler: the polynomial f(k) = k 2 − k + 41 yields primes for all the integers k with 1 ≤ k < 41. the sum of two squares (4 2 + 5 2), which makes it a centered square number. [4] the sum of the first three Mersenne primes, 3, 7, 31. [5]
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