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Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown whether there are infinitely many twin primes (the so-called twin prime conjecture ) or if there is a largest pair.
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
The convergence of the sum of reciprocals of twin primes follows from bounds on the density of the sequence of twin primes. Let π 2 ( x ) {\displaystyle \pi _{2}(x)} denote the number of primes p ≤ x for which p + 2 is also prime (i.e. π 2 ( x ) {\displaystyle \pi _{2}(x)} is the number of twin primes with the smaller at most x ).
Obama and Raul Castro reversed over 60 years of tension between the U.S. and Cuba by restoring diplomatic ties. 4. He urged states in 2013 to raise the minimum wage to $10.10 an hour.
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Every integer that can be written as the sum of two primes can also be written as the sum of as many primes as one wishes, until all terms are units. Goldbach was following the now-abandoned convention of considering 1 to be a prime number , [ 3 ] so that a sum of units would be a sum of primes.
The Riemann hypothesis ("the real part of any non-trivial zero of the Riemann zeta function is 1/2") and other prime-number problems, among them Goldbach's conjecture and the twin prime conjecture: Unresolved. — 9th: Find the most general law of the reciprocity theorem in any algebraic number field. Partially resolved.
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