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I knew the divisibility rule for 7, but my sir told me that these methods are known as recursion rules for divisibility. My sir also told them for 11, 13,17,19. But is there any logic behind it? Or is it just out of the blues?

BIS HD
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Of course there is logic behind it. Actually you have to learn about modular arithmetics to understand their proofs. This is not an out-of-the-sudden thing, as none is in mathematics. Actually you could derive visibility criteria for a lot of numbers, even for larger ones. See this thread.

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BIS HD
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  • Is the sequence of prime numbers also "not an out-of-the-sudden thing, as none is in mathematics"? – user66733 Nov 30 '13 at 11:38
  • Good point.. but actually.. I don't believe that it is an all of the sudden thing. Maybe we haven't understood the logic behind it yet? – BIS HD Nov 30 '13 at 11:42
  • Maybe as Euler believed no one would ever be able to understand the logic behind it? Regardless of what the answer to that question is, I guess none of us would live long enough to know what the actual logic behind it could possibly be. – user66733 Nov 30 '13 at 11:44
  • I'm pretty confident that mathematicians will eventually succeed in resolving the mystery of primes. But at least two bad things will happen: Neither will I be alive at that time nor will mathematics end with it. :-D – BIS HD Nov 30 '13 at 11:46
  • Actually 'mathematics won't end with it' is a good thing. A world without maths is such a miserable place to live in :| – user66733 Nov 30 '13 at 11:51
  • Well.. it depends on how stuck you are on your diploma thesis. :-P – BIS HD Nov 30 '13 at 11:54