Comments on: Narcissus prime

By: don s. mcdonald

don s. mcdonald — Fri, 09 Mar 2012 04:56:41 +0000

is prime 10^ 9000 000 000+3. false. try factor 1580 187 223. oeis. 2000. sci.math groups.google.com

By: Chris

Chris — Wed, 07 Mar 2012 09:57:30 +0000

This 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

David Harris — Wed, 07 Mar 2012 02:38:05 +0000

This 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

John Venier — Tue, 06 Mar 2012 01:31:23 +0000

@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

Adel — Tue, 06 Mar 2012 01:26:40 +0000

You 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

Luis — Mon, 05 Mar 2012 21:53:18 +0000

I don't have access to Mathematica at home, but interestingly using WolframAlpha with your expression produces False.

By: Rick Wicklin

Rick Wicklin — Mon, 05 Mar 2012 21:01:22 +0000

Palindrome 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

Mark Spencer — Mon, 05 Mar 2012 20:21:58 +0000

@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

John Venier — Mon, 05 Mar 2012 18:13:36 +0000

^ Except 11 of course, provided it is prime in the base in question.

By: John Venier

John Venier — Mon, 05 Mar 2012 18:13:04 +0000

My 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

John — Mon, 05 Mar 2012 15:43:28 +0000

The 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

Ted — Mon, 05 Mar 2012 15:39:04 +0000

Mathematica’s PrimeQ function might not be right. It isn’t always true. Though it usually is.