![]() There are a number of outstanding questions about perfect numbers. Today, even with vast computational power, only a total of 48 perfect numbers are known. The next number to be discovered has 37 digits are was discovered over 100 years later. The next perfect number wasn’t discovered until around 1500 years later – and not surprisingly as it’s 33,550,336.Ĩ,589,869,056 (discovered by Italian mathematician Cataldi in 1588)ġ37,438,691,328 (also discovered by Cataldi)Ģ,305,843,008,139,952,128 (discovered by Euler in 1772).Īnd they keep getting bigger. ![]() ![]() The first 4 perfect numbers are 6, 28, 496, 8128. Perfect numbers have been known about for about 2000 years – however they are exceptionally rare. This is easier to see with an example.Ħ is a perfect number because its proper factors are 1,2,3 and 1+2+3 = 6Ĩ is not a perfect number because its proper factors are 1,2,4 and 1+2+4 = 7 Perfect numbers are numbers whose proper factors (factors excluding the number itself) add to the number. You can use an online tool to test if numbers are happy or sad. Nrich has a discussion on some of the maths behind happy numbers. What are the happy numbers less than 100? Is there a rule which dictates which numbers are happy? Are there consecutive happy numbers? How about prime happy numbers? Can you find the infinite cycle of sadness? Numbers that don’t eventually reach 1 are called unhappy numbers.Īs an example, say we start with the number 23. Happy numbers will eventually spiral down to a number of 1. Happy numbers are defined by the rule that you start with any positive integer, square each of the digits then add them together.
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