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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Goldbach's conjecture is usually satisfied with one of the two primes being relatively small. The largest this smaller prime needs to be for numbers under 10^18 is 9341. This is part of the reason that there are so many ways to write even integers as the sum of two primes.
(There is one curio for this number that has not yet been approved by an editor.)
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