Comments on: Narcissus prime
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/
Applied Mathematics ConsultingMon, 16 Oct 2017 16:26:20 +0000hourly1By: don s. mcdonald
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4688
Fri, 09 Mar 2012 04:56:41 +0000http://www.johndcook.com/blog/?p=10892#comment-4688is prime 10^ 9000 000 000+3. false. try factor 1580 187 223. oeis. 2000. sci.math groups.google.com
]]>By: Chris
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4687
Wed, 07 Mar 2012 09:57:30 +0000http://www.johndcook.com/blog/?p=10892#comment-4687This came along at just the right time. My year 7’s have just been doing prime numbers so being able to discuss this particular prime was a bit of fun.
]]>By: David Harris
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4686
Wed, 07 Mar 2012 02:38:05 +0000http://www.johndcook.com/blog/?p=10892#comment-4686This looks cute, but there is nothing special about this number — it is basically random chance. By the Prime Number Theorem, the proportion of n-bit numbers which are prime is $~1/n$. Informally, if you generate “randomish” numbers with n bits there is a very high probability you will end up with a prime.
]]>By: John Venier
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4685
Tue, 06 Mar 2012 01:31:23 +0000http://www.johndcook.com/blog/?p=10892#comment-4685@Mark Spencer: Well, it was just a fun memory. Sheesh. Not all of us start out like Erdos. Present company excepted, of course.
]]>By: Adel
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4684
Tue, 06 Mar 2012 01:26:40 +0000http://www.johndcook.com/blog/?p=10892#comment-4684You can’t rely on alpha, it usually kills the process that would take more than a few seconds. Nevertheless, it is an amazing engine.
]]>By: Luis
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4683
Mon, 05 Mar 2012 21:53:18 +0000http://www.johndcook.com/blog/?p=10892#comment-4683I don’t have access to Mathematica at home, but interestingly using WolframAlpha with your expression produces False.
]]>By: Rick Wicklin
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4682
Mon, 05 Mar 2012 21:01:22 +0000http://www.johndcook.com/blog/?p=10892#comment-4682Palindrome primes I had heard of. But “upside down or in a mirror” is a new one. So the digits of this prime are invariant under right-left reading and also under the Klein four-group Z2xZ2. Who knew? [Assuming, of course, that “1” is written as “|”]
]]>By: Mark Spencer
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4681
Mon, 05 Mar 2012 20:21:58 +0000http://www.johndcook.com/blog/?p=10892#comment-4681@John Venier: Maybe you should have humbly said palindromes of even length are multiple of 11. And if by real math proof you mean 100..001 = 99..990 + 11, well… But hey, yeah, that’s nice, it works in any base, provided 9 is 10-1.
]]>By: John Venier
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4680
Mon, 05 Mar 2012 18:13:36 +0000http://www.johndcook.com/blog/?p=10892#comment-4680^ Except 11 of course, provided it is prime in the base in question.
]]>By: John Venier
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4679
Mon, 05 Mar 2012 18:13:04 +0000http://www.johndcook.com/blog/?p=10892#comment-4679My very first real math proof was that any palidromic prime must have an odd number of digits, which this one does, so there’s that for what it’s worth.
]]>By: John
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4678
Mon, 05 Mar 2012 15:43:28 +0000http://www.johndcook.com/blog/?p=10892#comment-4678The PrimeQ documentation doesn’t say whether it uses a probabilistic primality test, but given the size of the argument I thought it might.
]]>By: Ted
https://www.johndcook.com/blog/2012/03/05/narcissus-prime/comment-page-1/#comment-4677
Mon, 05 Mar 2012 15:39:04 +0000http://www.johndcook.com/blog/?p=10892#comment-4677Mathematica’s PrimeQ function might not be right. It isn’t always true. Though it usually is.
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