2023: Kick Off 2023 with Exciting Advances in Primality Testing 🎉

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Happy New Year! 2023 has at least one advantage over 2022 already: it could be prime! 2022 ends in an even number, so it's obviously even itself. That's called a divisibility test, and it's the same for determining if a number is divisible by 5: simply look at the last digit of the number. If that digit is a multiple of 2 or 5, then the original number is also a multiple of 2 or 5.

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There's another pretty well-known test for divisibility by 3, though it's slightly more complicated: add all the digits together, and if that sum is divisible by 3, the original number is also divisible by 3. If it's not obvious yet, you just repeat the process. In the case of 2023, the digits add up to 7, which is not a multiple of 3, so 2023 isn't either.

Seven also has a divisibility test, but in my experience it's a little less well-known than the tests for 2, 3, or 5. You take the last digit of the number, double it, and subtract that from the rest of the number. If that result is divisible by 7, then so is the original number. Just like in the test for 3, if it's not obvious whether the result itself is a multiple of 7, just repeat the process until it is.

#primenumbers #primality #divisibilitytests

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