Timeline for Does listing the prime factors always stop?
Current License: CC BY-SA 2.5
11 events
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| Jul 11, 2010 at 14:37 | comment | added | Wadim Zudilin | Nurdin's reference definitely confirms the obvious heuristics. Neverending list! And, as always with primes, nothing can be shown rigorously... | |
| Jul 11, 2010 at 14:36 | vote | accept | O.R. | ||
| Jul 11, 2010 at 14:21 | comment | added | O.R. | The independence of the base is that the question asks is for some number, in some base, the sequence never stops. Notice, for example that the remainders of the numbers appearing in the sequences (except the first one) in the division by the base (i.e. the last digit) correspond to possible last digits in that base. I have put a computer to run it in base 10 and all numbers end so far. Motivation? Just fun so far. | |
| Jul 11, 2010 at 14:20 | history | edited | Andrey Rekalo |
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| Jul 11, 2010 at 14:15 | answer | added | Nurdin Takenov | timeline score: 17 | |
| Jul 11, 2010 at 14:10 | comment | added | Charles Matthews | @Wadim: I agree. The better question would be to establish a heuristic based on the probability of primality of n being 1/log n, and the "normal" behaviour of prime factorisations. | |
| Jul 11, 2010 at 14:02 | answer | added | Wadim Zudilin | timeline score: 6 | |
| Jul 11, 2010 at 13:30 | comment | added | supercooldave | So: $4=2.2 \to 22 =2.11\to 211$ prime!! Have you written a program to do this? Does the chosen base matter? | |
| Jul 11, 2010 at 13:30 | comment | added | Wadim Zudilin | @Owen, that's the question: can you show that 12, 223 never stops? 223 is prime. @Franklin: there is no evidence (and no motivation!) for your question, especially because you claim that any base works. 77 (base 10) produces a very long sequence... | |
| Jul 11, 2010 at 13:26 | comment | added | Owen Sizemore | What do you mean by concatenate? So for example for 12, the prime factor are 2,2,3. The obvious meaning would result in the number 223. But this process will never stop. | |
| Jul 11, 2010 at 13:10 | history | asked | O.R. | CC BY-SA 2.5 |