Timeline for Bringing Number and Graph Theory Together: A Conjecture on Prime Numbers
Current License: CC BY-SA 2.5
9 events
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| Mar 23, 2010 at 15:15 | comment | added | Tony Huynh | @Hans - I wouldn't say that they are good candidates for counterexamples, only that for large graphs they would be the first thing I would investigate. This is simply because it's hard to get to grips with the condition for other large graphs (even say a large tree). As I said, I had no intuition for the problem initially, it just looked easier to find a counterexample than to prove it so I took the lazy man's approach. Actually, after Gerry and David's references I started to believe that the conjecture is true, and after Bjorn's answer, I really believe it. Nice question. | |
| Mar 23, 2010 at 15:07 | comment | added | Tony Huynh | Thanks David and Gerry for the references. Quite interesting. | |
| Mar 23, 2010 at 7:22 | comment | added | Hans-Peter Stricker | What's the intuition behind your surmise that large cliques, matchings or cliques together with an isolated vertex are good candidates for counter-examples? | |
| Mar 23, 2010 at 6:12 | comment | added | Gerry Myerson | A little more bibliographic detail on the paper David Hansen references: D K L Shiu, Strings of congruent primes, J London Math Soc (2) 61 (2000) 359-373. According to the review, the author proves that for any relatively prime $a$ and $q$, there exist arbitrarily long lists of consecutive primes, each congruent to $a$ modulo $q$. | |
| Mar 23, 2010 at 5:19 | comment | added | David Hansen | Yes, it has been proven - see MR1760689. | |
| Mar 23, 2010 at 4:29 | history | edited | Tony Huynh | CC BY-SA 2.5 |
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| Mar 23, 2010 at 3:15 | history | edited | Tony Huynh | CC BY-SA 2.5 |
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| Mar 23, 2010 at 2:17 | history | edited | Tony Huynh | CC BY-SA 2.5 |
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| Mar 23, 2010 at 1:47 | history | answered | Tony Huynh | CC BY-SA 2.5 |