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The Hardy-Littlewood prime k-tuples conjecture[18,29,34] and Erdos-Turan conjecture(every set of integers of positive upper density contains arbitrarily long arithmetic progressions)[14,15,16,17,20,35] are wrong.Using the circle method and the sieve method one do not prove simplest twin prime conjecture ( there exist infinitely many pairs of twin primes) and the simplest Goldbach conjecture (every even number N>4 is the sum of of two primes).Therefore from Hardy-Littlewood(1923) to 2013 all prime papers are wrong.They do not prove any prime problems. 2006Fields medal(Green-Tao theorem[20]),2007Wolf prize(Furstenberg theorem[15]) and 2012Abel prize(Szemeredi theorem[14]) are wrong,they do not understand arithmetic progressions.The correct arithmetic progressions is Example 8[6,p68-74].Institute for Advanced study(Math) has long been recognized as the leading international center of research in pure mathematics. Ann.of Math.published many wrong prime papers, for example:Green-Tao[20,41],Goldston-Pintz-Yildirim[38],Wiles-Taylor[48,49] and other. Their papers are related to the Hardy-Littlewood wrong prime k-tuples conjecture[18,29,34].Therefore their papers are wrong.But Ann.of Math reject Jiang papers. Editors of Ann.of Math do not understand the prime theory and want to publish wrong prime papers. Twin primes theorem[6,p341]. 2 1 2P P We have Jiang function to see example