Hi People,

Something to tie you over til next week:

Old man Winters was a quirky professor at our university, he was always coming up with strange notions.

One day he was talking to me and mentioned P'primes, I thinking he was stuttering, politely listened while he started listing the numbers 3.. 5.. 7.. and then I interrupted and asked what happened to two? He said "No, two is not a P'prime because it does not resonate properly, and, besides its even and no even number rightfully should ever claim to be a prime, let alone a P'prime."

He said he liked P'primes because it was a very sparse set, easily remembered, between 0 and 1000 there are only a dozen.

Realizing now, that he certainly was not talking about the set of primes since there was over a dozen between 0 and 50, I asked what the "P" was for and he said "Palindromic primes," he commenced listing the numbers again: "3, 5, 7, 17, 31, 73, 107, 127, 257, 443, 827... that's all there is between zero and a thousand... one dozen, nice and tidy."

I thought, and then said, "Hmmm, I count only eleven."

He paused and then said: "Yes, you are right, I missed one. How forgetful of me."

Which P'prime number was missed?

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11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, and 929 were all missed. I believe these are all the palindromic primes below 1000. But I could be wrong.

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BlueTurbit wrote on Wed, 05 November 2003 13:31

11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, and 929 were all missed. I believe these are all the palindromic primes below 1000. But I could be wrong.

Old man Winters was not very fond of decimal numbers.

[Updated on: Wed, 05 November 2003 15:21]

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[Updated on: Wed, 05 November 2003 15:56]

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donjon wrote on Wed, 05 November 2003 15:09

Well, assuming Old man Winters is not crazy... {which may be a big assumption} His list of P'primes has 3,5,7... which are not in the set of so called palindromic primes... in fact, none of his numbers are palindromic in the normal sense. So, maybe you need to shift perception.

IMO we're all wrong. Winters is wrong in that all those other numbers above 7 are not palindromic primes according to definitions on several websites I visited. Or possibly you quoted him wrong?
You are wrong as you listed them also. You are also wrong assuming because he's old and/or a professor that he is right. I have heard lots of professors commenting on news programs on various issues that I think are both wrong and crazy IMO.
Ron is wrong in that he said I was right. Wrong!
I was wrong because I let myself get distracted by the old man's comment and forgot about the even number 2 along with 3, 5, 7, 11... is also in the group of palindromic primes.

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Hatterson wrote on Wed, 05 November 2003 17:21

No acutually, not everyone is wrong. You, in fact, are all right in your own way. However you are thinking of numbers differently. You are thinking in base ten and donjon and old man Winters are in BINARY. Yes, I said binary... Seeing Donjon's comment about shifting perception I thought about converting the numbers into binary. 3 = 11 5 = 101 7 = 111 17 = 10001 73 = 1001001 107 = 1101011 127 = 1111111 257 = 100000001 443 = 110111011 827 = 11001110011 If you notice those are all palindromes (in binary). Therefore the missing P`prime is....100111001 or for those of you who like base 10, 313 which ironically is also a base ten palindrom. Nice riddle, very interesting

Chuckle... yes, 827 is NOT palindromic... excuse me, however, 313 is and shares the double distinction of being palindromic in both base ten and base two.

BTW: thanks Ron for the link to those prime pages... I'm now running a program which is calculating base10+base2 palindromic primes... very cool

[Updated on: Wed, 05 November 2003 21:50]

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Ummm, sorry. Wrong door. I'm not supposed to be in here, I think.

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donjon wrote on Thu, 06 November 2003 15:48

313 is <snip> palindromic in both base ten and base two. BTW: thanks Ron for the link to those prime pages... I'm now running a program which is calculating base10+base2 palindromic primes... very cool

So out of curiousity...what is the next lowest Prime Number that is palindromic in both base 10 and 2?

Is your program extinsible to other (combined?) bases?
The lowest prime palindromic in all the bases 2-10 perhaps?

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gible wrote on Fri, 07 November 2003 10:03

Is your program extinsible to other (combined?) bases? The lowest prime palindromic in all the bases 2-10 perhaps?

That may be a tad high !
Maybe the lowest palindrome (other than 0 and 1) in all the bases 2-10 might be expressible to humans.

I am happy to be shown an answer either way of course.

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gible wrote on Fri, 07 November 2003 04:03

So out of curiousity...what is the next lowest Prime Number that is palindromic in both base 10 and 2??

So far, my list of palindromic[base2+10] primes is:
3, 5, 7, 313,
7284717174827 [1101010000000011010111110101100000000101011]

and that is it.... (my program is running 100% of the time)

*snip*

Is your program extinsible to other (combined?) bases? The lowest prime palindromic in all the bases 2-10 perhaps

Its certainly possible to extend it... the numbers are stored in character format (allowing for a precision of 256 digits at the max I think, however using malloc that may possibly be increased) the base is not the limitation... time is.

The program is still examining 19 digit (base 10) numbers right now.

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zoid wrote on Fri, 07 November 2003 07:45

Ummm, sorry. Wrong door. I'm not supposed to be in here, I think.

I think I just broke a rib from laughing

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Hi,

I'm now running a program checking for Prolific Palindromic Primes:

It checks a prime number to see if it is palindromic in any of the bases (2-16) and spits out the number if it is palindromic in more than one base. Excluding the trivial cases (2-17) the most interesting numbers having palindromic values in more than two bases are:
Number:191 Bases: 6 9 10
Number:257 Bases: 2 4 7 16
Number:313 Bases: 2 10 13
Number:337 Bases: 9 14 16
Number:353 Bases: 10 13 16
Number:373 Bases: 4 8 9 10
Number:787 Bases: 4 10 11 16
Number:797 Bases: 10 12 13
Number:1667 Bases: 3 5 12
Number:1913 Bases: 3 14 15
Number:2293 Bases: 5 6 14
Number:65537 Bases: 2 4 16
Number:356981 Bases: 2 14 16
Number:1181729 Bases: 3 4 9
Number:1311749 Bases: 2 4 8
Number:50339843 Bases: 4 8 16
Number:83914757 Bases: 2 8 16
Number:89466197 Bases: 2 8 16



I have noted that these palindromes seem to group in families of two types:
Close bases like base 10 and base 11
Power bases like 2,4; 2,8; 2,16

It looks very unlikely that there will be a palindromic prime which is palindromic in all bases. (that would be the ultimate

[Updated on: Sat, 15 November 2003 19:10]

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Well yes...I encountered a similar problem experimenting for one of my number theory assignments a few months ago. Even after I recoded my mathematica script it still had O(n^2) runtime. Of course we didn't think to question it...it worked fine for 10,000. We left it going for 100,000 for 4 hrs and then figured the runtime at 3.8 months (I think).

And after all of that I can't even find the assignment to tell you the wonderful 99.4% accurate formula

Edit: PS my last exam today YIPPEEEE!!!!!!

[Updated on: Tue, 11 November 2003 01:57]

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zoid wrote on Tue, 03 February 2004 04:24

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Rather than free form math, I prefer "Martian Math."
3+3+3=6
WHAT?!?
I don't like that 6 there...
6
3+3+3=9
There, all better now.
Or another example...
3+3-3=6
Hmmm...
-3
There, no more -3!
3+3 =6

(I just love my smilies )

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