Perfect Number Finder

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A perfect number is an integer which has a factor sum equal to twice the number.
The first perfect number is 6, as its factors add up to 12 ( = 1+2+3+6 )
The second perfect number is less than 30, so you should be able to find it quite quickly, using the 'Finder'.
However, then there is a rather mystifying gap, until you reach the next (more than 400, less than 600),
The fourth number is reached after another big gap, (it's over 7000, under 9000),
but then, the fifth is more than 30,000,000!!!!
Can you work out what's going on?? Or 'investigate further', as all good task sheets say....

If I've got around to it, a solution should be lurking at the other end of this link

If you want to empty the boxes, the 'Clear the boxes' button lower down will help.
Oh, and when you want to clear away the factor tables if the page has got rather long, just reload the page.

What can be entered? What can't be entered?

Factor Sum