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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.
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