In Java

According to the conjecture of Goldbach (1690-1764), every even nuriber greater than two is the sum of two prime numbers. For example, 24-5 + 9. This may occur in several different ways: 24-7+17 11 + 13. This is one of the oldest unsolved problems in number theory and in all mathematics. There were rigorous results made by a host of mathematicians to prove cases for the conjecture. In 1966, Jingrun Chen2 showed that every sufficiently large even integer can be written as r +y where z is a prime and y is either prime or product of two primes. Chen's theorem is a giant step towards the Goldbach conjecture, and a remarkable result of the sieve methods. Number theorists believe that we are close to a solution of Goldbach's conjecture, though the last (small) step is often the hardest, for which the conjecture remains open to this date. What to do The goal of this project is to verify the conjecture with computer technology. In this project, you are to write a program that outputs the decomposition of an even integer2) into the sum of the two primes, where the first entry is as small as possible and the last is as larger as possible. More precisely, you program should read an upper and lower bound for the range of even numbers and is expected to generate all such decompositions for those even integers within the range as the following output listing: Sample Run #1 ILLUSTRATING GOLDBACHS CONJECTURE FOR NUMBERS 4= 2+2 10 3 7 16-3 13 22 = 3+19 28 5 23 34= 3+31 40= 3+37 46 3 + 43 52 = 5+47 58-5 + 53 64 = 3+61 70 3 67 76373 82 3 79 88 = 5+83 945 89 1003 97 106 3 103 112 = 3+ 109 6# 3+3 12 = 5+7 18 = 5 + 13 24- 5 19 30 = 7+23 36 = 5+31 42 5 37 48 = 5+43 54-7 47 607 53 66-5+61 72 5 67 78 573 14 = 3+11 20-3 17 263 23 32 = 3+29 38 7 31 44-3+ 41 50= 3+47 56 3 + 53 62 3 59 68 = 7+61 74 = 3+71 807 73 86 3 83 92 3+89 98 = 19 + 79 104 3 101 110 = 3 + 107 90783 96 7 89 102 5 97 108 5 103 114 = 5 + 109 116 3+ 113