![]() ![]() (See Tony Forbes' web page for more information.) The longest known arithmetic sequence of primes is currently of length 25,Īnd continuing with common difference 366384*23#*n, found by Chermoni Raanan and Jaroslaw Wroblewski in May 2008. Obviously this is not optimal! It is conjectured ![]() įinally, in 2004, Green and Tao showed that there are indeed arbitrarily long sequences of primes and that a k-term one occurs before : Many triples of primes in arithmetic progression. In 1939, van der Corput showed that there are infinitely Such primes sequences there should be for any given length-HardyĪnd Littlewood first did this in 1922. Together these two sequences contain all of the primesĪ related question is how long of a arithmetic sequenceĬan we find all of whose members are prime.Īnswer should be arbitrarily long-but finding long sequences ![]() Then the corresponding infinite sequence contains infinitelyĪn important example of this is the following two If a 0 and d are relatively prime positive integers, In general, the terms of an arithmetic sequence withĪ n = dn+ a 0 ( n=0,1,2.). Using a common difference of 4 we get the finiteĪrithmetic sequence: 1, 5, 9, 13, 17, 21 and also the infinite sequenceġ, 5, 9, 13, 17, 21, 25, 29. Is a sequence (finite or infinite list) of real numbers for whichĮach term is the previous term plus a constant (called the commonĭifference). An arithmetic sequence (or arithmetic progression) ![]()
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