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Oct 02
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Here’s an impressive example of number crunching (and pushing current hardware to its limit). A team in the UK resolved the Congruent Number Problem which was first posed about a thousand years ago for the first 10^12 (one trillion) cases. The problem with this solution is that the numbers are just too large to fit into conventional computer memory so the researchers had to do some creative work with hard drives.
For the uninitiated, congruent numbers are the whole number areas of right angled triangles whose sides are either whole numbers or fractions. For example, a 3-4-5 right angled triangle has an area of 6, which is a congruent number. All counted, the researchers found 3,148,379,694 congruent numbers in the range up to 10^12. Impressive going, but it doesn’t quite give you the rock star status of finding the next largest prime number!