Strange Numbers

[IrishEyes]

if you guys keep this up, we're going to have to add a MATH forum...
seriously though, this stuff is awesome. you guys just blow me away!

[maddog]

Irish,

I have begun to think of this thread moving to the Physics/Math forum.

Turtle,

I told my friend about 304 bieng the product of 2^4 and 19. He did think that wierd. From
him restating the definition of Wierd numbers and the lowest one being 70, I see these are
definitely different kind of numbers.

In the meantime, I found some websites on a related subject of Mersenne primes and perfect
numbers.

http://mathworld.wolfram.com/PerfectNumber.html
http://www.utm.edu/research/primes/mersenne/
http://www-groups.dcs.st-and.ac.uk/~...t_numbers.html
http://mathforum.org/dr.math/faq/faq.perfect.html

I have thought about it and figure that any normed division ring where the modulus was
used to calculate as you have wouldn't work directly. However, there is curiousity based
on one of the above websites ==> what would the numbers you found look like in other
bases ?

Maddog

[Turtle]

Yes, I think moving to Math section is good; I didn't know how to do it. I believe I was visiting just those links you listed when I found Hypography! As I have worked a lot in other bases & have written software to operate in base 2 to 29, in which base of this range would you like to see the list of Strange Numbers? Now I do use the convention for bases over ten of J=10, K=11 etc & I am discussing this in another thread. Nonetheless, the approach you suggest Madddog is very good. I don't like to type long posts, but I think this moves us forward.

[Turtle]

Just a short addendum: About the time I started this thread, I started an experiment run in factoring as I described above. It is written in compiled Basic(TurboBasic by Borland, now extinct) & running on a non-net 200mghz pentium in a DOS window under Windows 95. At this post I have factored slightly over the first 6 million integers. The results I view real time on my screen & I have a trap to display numbers deficient between 0 & -2000. I'm looking of course for some kind of corallery deficient sets to those I described as Strange etc. Anyway, I happened to look up & find this number caught in the trap I just described: 6,123,584. It is defficient by 304! It has 28 proper divisors(I didn't trap what they were, only how many). So in the interest of keeping my experiment run going while we discourse, I have to raincheck on printing the list of Strange into other bases for you. Perhaps someone wants to take that on & post it?

[maddog]

Originally Posted by Turtle

Yes, I think moving to Math section is good; I didn't know how to do it. I believe I was visiting just those links you listed when I found Hypography! As I have worked a lot in other bases & have written software to operate in base 2 to 29, in which base of this range would you like to see the list of Strange Numbers? Now I do use the convention for bases over ten of J=10, K=11 etc & I am discussing this in another thread. Nonetheless, the approach you suggest Madddog is very good. I don't like to type long posts, but I think this moves us forward.

The convention for any bases higher that 10 is to use A thru Z for bases 11 to 36. For
higher you could upper/lower case... for base 62.

1 .. 9, A .. Z, a .. z : be 1 .. 61 for base 62.

I would think interesting bases would be of prime, perfect or strange order. Thus of
interest would be

bases: 6, 7, 11, 12, 13, 17, 19, 24, 28, 36, 56, for starters. Some of these would be of
interest to me directly in physics, namely: 6, 7, 11, 12, 13, 24, 28, 56.

I don't know what pattern may form. I just feel it might be interesting.

Maddog

[IrishEyes]

Thread moved to Physics/Math Forum

Keep crunching those numbers...

[Turtle]

Thanks Irish. So before moving on to another topic, do I understand maddog that you & your friend now believe I found something previously undescribed? I just want to be sure I'm advancing from a solid base. (Hahahaha; that's math humor!)

[maddog]

Originally Posted by Turtle

Thanks Irish. So before moving on to another topic, do I understand maddog that you & your friend now believe I found something previously undescribed? I just want to be sure I'm advancing from a solid base. (Hahahaha; that's math humor!)

Enough that you have intrigued him and that he has heard of this and he was at the last Forum on Number
Theory just three weeks ago in Las Vegas!

BTW, he and the website I mentioned has stated the holy grail (oldest known) of conjectures that (drum
roll please)...

All perfect numbers are even... Ta Da!!!

This one has been in search of an answer either way since Pythagorus' time. By way of example of an
Odd Perfect Number or that one Definitely DOESN'T exist. Were you to prove/disprove that, you could be
famous!

Maddog

[Turtle]

Indeed it is a holy grail. I thought I had proved it a couple years ago & I was furious on the trail of the beast. Alas, I was off by one. In the past when I told mathemeticians about these Strange Numbers (I have a few since I found this in '97, '98) I just gave the list & made them try to guess & figure it out & I never came clean & told. I also submitted a paper on them to a math journal, but it was rejected. Now, I am of the mind to share it all freely because of Tormod's Hypography &, well...it doesn't seem right to keep it to myself.
Now back to some numbers:
The First Ten Elements Of Set P (Peculiar numbers) A number is Peculiar if the sum of its proper divisors is 992 greater than itself. {1488, 2480, 2892, 3472, 5456, 6104, 6448, 8432, 9424, 11408, ...}
Most Peculiar Numbers are of the form 496 (a perfect number) times a prime.
Between 1 & 12,000,000 exist ten Peculiar Numbers which have no Perfect divisors. They are: 2,892; 6,104; 170,612; 458,144; 857,312; 1,006,496; 1,764,512; 4,041,152; 9,865,304; 11,627,864

I just saw the other day on web the latest Perfect Number found; over 700 thousand digits!

[Turtle]

Some more Numbers, this time , anamolous Bizarre Numbers. Again briefly, a Bizarre Number is defined as any integer whose sum of its proper divisors excede it by 56(56 is twice the perfect28). A listof the first 60 Bizarre Numbers is attached to post #1 of this thread.
So, again, most elements of this set may be generated by multiplying the perfect number 28 by a prime, but this does not find all the members of the set & those it does not find I call anomolies. You must factor all the integers & make the comparison to the set definition. Here is a list of the anomalous Bizarre Numbers between 1 & 12,000,00:
{4,544; 9,272; 14,552; 25,472; 74,992; 495,104; 6,019,264...}
Who can be the next to add to the list?