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Recreations in the Theory of Numbers
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| ...but poorly written. It's very interesting in a historical sense. For instance, Table 9 shows composite Mersenne's numbers up to n=251, most of them with question marks when a factor wasn't known to be composite or prime, and C when it was known to be composite but the factors weren't known. For instance, 2^101-1 was known to have at least 4 prime factors, but no factors were known. At the time (1964-1966), ENIAC was being used to compute such things. Yesterday, on my lowly Pentium 4, using Mathematica's built-in functions, I factored all the numbers completely in less than 45 minutes of computation time. One of them (2^251-1) took 34 minutes and 7 seconds and another took 5 minutes 10 seconds -- all the rest were very fast. It's amazing how much better the algorithms and computers are, today. |
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