Comments by "disgruntledtoons" (@disgruntledtoons) on "The Reciprocals of Primes - Numberphile" video.

  1. A minor correction. In the first example you referred to 7 as the dividend. The term for the number being divided into the other is the *divisor*; the number into which it is divided is termed the dividend.
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  2. Also, for each prime, the repeat period is either p-1 or some number that divides into p-1.
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  3. Also, there is a practical application of finding the repeat period. You can convert some text into an integer (by concatenating the codes into a massive integer), and divide that integer by a smaller number. The remainder becomes a checksum for that text. The best divisor for this is a prime with the longest repeat period when dividing binary numbers.
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  4. Another way to approach the same issue is to take the prime factorization of (10^n)-1. Counting only the primes that were not in the factorization for lower values of n, you get 3 when n = 1, 11 when n = 2, 37 when n = 3, 101 when n = 4, and so on.
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