Timeline for Statements with rare counter-examples [duplicate]
Current License: CC BY-SA 3.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 27, 2014 at 23:55 | comment | added | Bennett Gardiner | However, Littlewood (1914) proved that the inequality reverses infinitely often for sufficiently large $n$, and Skewes then showed that the first crossing point must occur before $$n= 10^{10^{10^{34}}}$$ which is now known as Skewes number. This bound has since been lowered to $10^{371}$. | |
| May 27, 2014 at 23:55 | comment | added | Bennett Gardiner | One of the important surprises in number theory that I like, Gauss' updated approximation for the number of primes below $x$, $$ \pi(n) \sim \operatorname{Li}(n) = \int_2^n\frac{\mathrm{d}x}{\ln x}. $$ For all values of $n$ that we can check, $\pi(n) < \operatorname{Li}(n)$. "As a result, many prominent mathematicians, including no less than both Gauss and Riemann, conjectured that the inequality was strict." | |
| May 27, 2014 at 23:30 | history | closed | Jack M CommunityBot Michael Albanese Hakim user85798 | Duplicate of Examples of patterns that eventually fail | |
| May 27, 2014 at 22:14 | comment | added | GarouDan | The best example that I know is the Gauss conjecture about two curves, that Liouville proved he was wrong. The number that proves Gauss was wrong is estimated to be ridiculously long. Some day I wrote an answer =) | |
| May 27, 2014 at 20:28 | answer | added | MJD | timeline score: 7 | |
| May 27, 2014 at 18:00 | answer | added | Toscho | timeline score: 6 | |
| May 27, 2014 at 17:52 | answer | added | Toscho | timeline score: 4 | |
| May 27, 2014 at 11:39 | answer | added | miket | timeline score: 4 | |
| May 26, 2014 at 23:59 | review | Close votes | |||
| May 27, 2014 at 1:15 | |||||
| May 26, 2014 at 23:36 | comment | added | Jack M | $\prod_{i=0}^n(x-i)$ is zero for $x=0, ... n$ but not thereafter. | |
| May 26, 2014 at 17:46 | answer | added | David H | timeline score: 5 | |
| May 26, 2014 at 17:02 | comment | added | David Richerby | @gnasher729 And every positive integer divisible only by 1 and itself is prime! | |
| May 26, 2014 at 16:32 | comment | added | gnasher729 | All prime numbers are odd :-) | |
| May 26, 2014 at 14:05 | comment | added | Viktor Vaughn | There are some nice examples in this thread. | |
| May 26, 2014 at 14:00 | answer | added | sas | timeline score: 24 | |
| May 26, 2014 at 13:57 | comment | added | daniel | This rings a bell...duplicate? | |
| May 26, 2014 at 13:37 | answer | added | Platonix | timeline score: 11 | |
| May 26, 2014 at 13:24 | comment | added | André Nicolas | If $p$ is prime, then $2^p-1$ is not divisible by $p^2$. See Wieferich primes. | |
| May 26, 2014 at 13:21 | comment | added | Platonix | Fermat's Last Theorem is proven true... | |
| May 26, 2014 at 13:15 | comment | added | André Nicolas | The number of primes $\le x$ of the form $4k+3$ is never greater than the number of primes $\le x$ of the form $4k+1$. Please see Prime Number Races. Counterexamples are actually not rare, but the first one is big. | |
| May 26, 2014 at 13:01 | answer | added | Batman | timeline score: 50 | |
| May 26, 2014 at 12:56 | comment | added | Amzoti | See the prime generating polynomials: mathworld.wolfram.com/Prime-GeneratingPolynomial.html | |
| May 26, 2014 at 12:53 | history | asked | Leif Sabellek | CC BY-SA 3.0 |