Re: [math-fun] Favourite prime numbers
Mike Stay>My favorite prime is 1+i. One good reason: It's the base of a binary number system, with bits 0 and 1, that can represent all complex numbers (without needing a sign bit). The pure fractions represent a simply connected region coincident with the twindragon fractal (File:Dragon_tiling5.svg <http://en.wikipedia.org/wiki/File:Dragon_tiling5.svg>) . --rwg Start with 0. Then iterate Union[%, 1 + %]/(1 + I); a few times. Then ListPlot[{Re[#], Im[#]} & /@ %, PlotStyle -> PointSize[Large]] On Fri, Jun 3, 2011 at 3:01 PM, <rcs@xmission.com <http://gosper.org/webmail/src/compose.php?send_to=rcs%40xmission.com>> wrote:> Let's not forget 314159! --Rich>> -----> Quoting Thane Plambeck <tplambeck@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=tplambeck%40gmail.com>>:>>> 149459, a prime number, the period of the octal game 0.16>>>> It magically appeared in the green phosphor of a DEC VT100 in the>> Stanford CS department basement in the fall of 1986>>>>>>>> On Fri, Jun 3, 2011 at 6:26 AM, Victor Miller <victorsmiller@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=victorsmiller%40gmail.com>>>> wrote:>>>>>> My favorite prime is 144169. Besides the fact that it looks like 12^2>>> concatenated with 13^2, it's also the discriminant of the quadratic field>>> which contains the eigenvalues of the Hecke operators on modular forms of>>> weight 24.>>>>>> Victor>>>>>> On Fri, Jun 3, 2011 at 8:49 AM, Dan Asimov <dasimov@earthlink.net <http://gosper.org/webmail/src/compose.php?send_to=dasimov%40earthlink.net>> wrote:>>>>>>> (((>>>> My favorite number is 24 hands down, because>>>> of its amazing properties like showing up>>>> in Dedekind eta, 1^2 + ... + 24^2 = 70^2>>>> being the only such relation, the 24-dimensional>>>> Leech lattice, and 24 being the largest number N>>>> such that all smaller numbers K with GCD(K,N) = 1>>>> satisfy K^2 == 1 (mod N). At least some of these>>>> are interconnected.>>>> )))>>>>>>>> But how about prime numbers? After the first few,>>>> how do you distinguish, say, 101, 103, 107, 109 ?>>>> Are there standard measures of some sort that>>>> distinguish among prime numbers?>>>>>>>> --Dan>>>>>>>> Sometimes the brain has a mind of its own.>>>>
I think you need a sign bit for radix 1+i. Knuth likes i-1, which doesn't need the sign bit. Rich --- Quoting Bill Gosper <billgosper@gmail.com>:
Mike Stay>My favorite prime is 1+i.
One good reason: It's the base of a binary number system,
with bits 0 and 1, that can represent all complex numbers
(without needing a sign bit). The pure fractions represent
a simply connected region coincident with the twindragon
fractal (File:Dragon_tiling5.svg <http://en.wikipedia.org/wiki/File:Dragon_tiling5.svg>) .
--rwg
Start with 0. Then iterate
Union[%, 1 + %]/(1 + I); a few times. Then
ListPlot[{Re[#], Im[#]} & /@ %, PlotStyle -> PointSize[Large]]
On Fri, Jun 3, 2011 at 3:01 PM, <rcs@xmission.com <http://gosper.org/webmail/src/compose.php?send_to=rcs%40xmission.com>> wrote:> Let's not forget 314159! --Rich>> -----> Quoting Thane Plambeck <tplambeck@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=tplambeck%40gmail.com>>:>>> 149459, a prime number, the period of the octal game 0.16>>>> It magically appeared in the green phosphor of a DEC VT100 in the>> Stanford CS department basement in the fall of 1986>>>>>>>> On Fri, Jun 3, 2011 at 6:26 AM, Victor Miller <victorsmiller@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=victorsmiller%40gmail.com>>>> wrote:>>>>>> My favorite prime is 144169. Besides the fact that it looks like 12^2>>> concatenated with 13^2, it's also the discriminant of the quadratic field>>> which contains the eigenvalues of the Hecke operators on modular forms of>>> weight 24.>>>>>> Victor>>>>>> On Fri, Jun 3, 2011 at 8:49 AM, Dan Asimov <dasimov@earthlink.net <http://gosper.org/webmail/src/compose.php?send_to=dasimov%40earthlink.net>> wrote:>>>>>>> (((>>>> My favorite number is 24 hands down, because>>>> of its amazing properties like showing up>>>> in Dedekind eta, 1^2 + ... + 24^2 = 70^2>>>> being the only such relation, the 24-dimensional>>>> Leech lattice, and 24 being the largest number N>>>> such that all smaller numbers K with GCD(K,N) = 1>>>> satisfy K^2 == 1 (mod N). At least some of these>>>> are interconnected.>>>> )))>>>>>>>> But how about prime numbers? After the first few,>>>> how do you distinguish, say, 101, 103, 107, 109 ?>>>> Are there standard measures of some sort that>>>> distinguish among prime numbers?>>>>>>>> --Dan>>>>>>>> Sometimes the brain has a mind of its own.>>>> _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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