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November 9, 2015 08:00 pm

Interviews: Ask Mathematician Neil Sloane a Question

Considered by many to be one of the most influential mathematicians alive today, Neil Sloane has made major contributions to the fields of sphere packing, combinatorics, and error-correcting codes. He is probably best known for being the creator and curator of the On-Line Encyclopedia of Integer Sequences (OEIS), known simply as “Sloane” by its many users. The repository is over 50 years old and contains over 260,000 sequences. Neil recently turned 76 but his passion for mathematics remains as strong as ever. Talking about a recent project, he writes: “Back in September I was looking at an old sequence in the OEIS. The sequence starts 1, 12, 123, 1234, 12345, ..., 123456789, 12345678910, 1234567891011, ... The n-th term: just write all the decimal numbers from 1 to n in a row and think of this as a big number. The entry for the sequence had a comment that it is expected that there are infinitely many terms which are primes, but that no prime was known, even though Dana Jaconsen had checked the first 64,000 terms. So I asked various friends and correspondents about this, and people extended the search somewhat. In fact Ernst Mayer has set up a cloud-source project to look for primes in the sequence, and the sequence has now been checked to nearly n = 270,000 without finding a prime. But I am hopeful that a prime will appear before we get to n = 10^6. When a prime is found, as it surely will be, it probably won't be the largest prime known, but it will be close to the record (which is held by the latest Mersenne prime). We may make it into the top ten. It will certainly be the largest known prime which is easy to write down! (Explicitly, I mean. You may know that 2^32582657-1 is prime, but you won't be able to write down the decimal expansion without using a computer).” Neil has agreed to take some time away from his favorite sequences and answer any questions you may have. As usual, ask as many as you'd like, but please, one question per post.

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