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Amazing but totally unaplicable maths

What puzzle has been worked on continually for more than 2000 years, has no practical application, and will probably never be solved? The answer: the search for the definitive of perfect numbers. The mathematicians of ancient Greece attributed characters to numbers and awarded some the status of perfection. For Euclid, one of the founding fathers of mathematics, a perfect number was one that equaled the sum of its own divisors - that is numbers that will divide into it without leaving a remainder. The first number is 6: its divisors are 1, 2 and 3, which add up to 6. The second is 28 (1+2+4+7+14). The Greeks new only two other perfects: 496 and 8,128. More than 1500 years later, in the 15th century, the existence of a fifth perfect number was announced: 33, 550, 336. Four additional perfect numbers were discovered in the next three centuries. But such was their rarity that in 1811 the mathematician Peter Barlow confidently stated that the ninth perfect number, one with 37 digits, "is the greatest that will ever be discovered…..It is not likely that any person will attempt will attempt to find one beyond it." But in 1876 Barlow was proved wrong when a 10th perfect number was found, consisting of 77 digits. Today the list has been greatly extended and is still constantly growing. The largest known perfect number, the 27th, has a staggering 26,790 digits; it was revealed, with the help of a computer in 1979.