Just for fun my quest to find a star compressor.

• The aim was to find the ultimate data compressor. As data & information has made us what we are today and with computers the way they are, there is so much information on just about anything and everything we have had the stone age, iron age and so on but now we are in the information age, and the Internet has taking over from books as the main information store, as it takes time & space to hold all this information it would be nice if it was possible to compress the data until it was needed, yes there are zippers on the market but they are not much good with raw data like MP3 files, maybe about 2 or 3% can be zipped but it can take longer to download a music file then it takes to play it. "this was before broadband"  It would be good if you could download a 1k byte file that opened up in to a 1 megabyte file, for example n/100019 that is only 6 digits to give a 100018 digits of data, I have printed this number out 100019 Prime , As it was computers that stored this information, then it was computers that I was going to try and find the solution to this problem, computers use mainly 8 bits equal to one byte of data and one byte equals one character, I was going to look for something that could add up number from 0 to 2^8=256 and then return them back again. Example an A4 page of text would use about 80 characters per line, there are about 60 lines per page 80x60 = 4800 bytes of data without the control characters. Memory used is just over 4k bytes,

  • Now if it was possible to add all of the characters up on that page it would give a number less then 90x4800= 432000. This number would only take up 4 bytes of data using binary numbers or 6 digits as above. This means that all the information on that A4 page is now hidden within this number, giving approximately a reduction of 4800/4 = 1200. That is less then 0.1%. That looks good, but how do you get the information back...!

• It would not take anyone long to work out that it is impossible with just adding up 10 base numbers and then to undoing them.

• So I tried binary and soon found that every number has an equal opposite. Even at a 1 bit level you still had a 50% chance (yes or no)... So this told me that I was looking for something that has less then 1 bit. Or a third bit, Is this possible....?

• I tried using 2x 1 bit to make a bit less then 1 bit always comeback as 1 bit so it was back to what I discovered above. So I tried 3x 1 bit. This looked hopeful as I now have 1/3 2/3 or 3/3. More than Yes or No - a Maybe as well. But it can also equal 2^3=8 which can be divided by 2. Yes or No again ..!! At this point I started to think that there will never be a solution to this problem. Unless you could find something that could give you that something that was not a yes or a no.!!! What is that third thing..

The name star compressor come from the third thing

• So this led me to a possible third polynomial, a few years ago I had to write a program that would revise a third polynomial just using machine code as it needed to be fast… It was quite easy after I had found out the basics about polynomial. I don't know if any one else has tried it, I would like to know? I fitted it into less then 750 bytes of machine code. Boy it was quick, and with out a math's coprocessor...

  • I played with ploy's for a few days and got nowhere. At this time I was running a small computer company and it was getting very busy so I put the star compressor to one side.

• Up to now everything I have tried could be revised so I was looking for something that would not revise the same way I put it together, Anyway some time had passed and I have moved on from the computer company and I am taking life a bit easier now, then on the TV there was a bit about the public lock, where you need a different code to unlock the data to what you used to lock it, were have I been? Is this what I have been looking for? ... A few years ago some company (no names) said "we have found the best encryption ever", It was 2048 bits long, It took me less then 15 minutes to write a program to find the key to unlock it… everything has an equal opposite....!!! Unless it’s zero..? This is what I have found, So I found out about the public lock it was not the answer 

DAY ONE new quest

• So I had a play with prime numbers, the first thing I did was to write a program that would give me all the prime numbers from 1 to 250,000 The program was good it took less than 5 seconds to run, it gave me all the known prime numbers from 1 to 250,000. I printed them out on to 49 A4 pages! It was well worth the half hour it took to write the program... I have put those numbers in a text file so you can see them.

• I started to play with these numbers and soon realise that there was a link between some prime numbers. I started to calculate where the next prime number would be, and yes there it was, I had found a way of finding new prime numbers. As I said before everything has an equal opposite, so could I work a prime number backward! As far as I am aware this has not been done before.. "Yes I could " 

• My claim to the largest prime number  I have calculated to date is. 

• 2^170,141,183,460,469,231,731,687,303,715,884,105,727-1

I would like to add an UPDATE here Dec. 2009, I have seen many articles about the above prime number, things like "this number has been know for some time"," it's already been found", plainly these people do not understand raised to the power of 2, the highest number in the Guinness book of records to date is: 2^43,122,609-1 just by looking at the two numbers I think you can see that my number is many times larger. It will take many years before it is proofing that this is a prime as it is to big for even a supper computer to work out, but I have also seen that wikiped.org have use some of my data and clamed it as their own, but what else would you expect from an American, they famous for stealing other peoples information like BELL did.

• Mathematical notation which denotes two multiplied by itself by the above number minus one. This number is now being tested, the first person to confirm this prime number would join me in the Guinness book of records and a clam to the largest prime number  ... I have registered this number with the Guinness world records just in case 2nd Nov 2000. so don't try to cheat me.

• I think it holds the key to many other math's problems…. As in problem Christian Goldbach 1742 ?.

  • I have never researched prime numbers so I have nothing to compare my data with, I will get a book out when I have finished, to see if it can help me more, It is possibly a good thing to start from scratch, as you are not relying on others, and it is a best way forward. All I know about Prime numbers is that they can only be divide by 1 and itself, and it is this information I programmed in to my computer, it gave me all the prime numbers from 1 to 250,000 the rest is me working out what is going on.

This is some of what I have found, about prime numbers...

First look

1) prime number 2 is the only even prime number and has not got recurring digits.

½ =0.5 "this is important"

2) prime number 3 has recurring digits

1/3=0.333, "this is important"
2/3=0.666,

3) Prime number 5 is the only prime number when divided by any number gives an even number and has not got recurring digits.

1/5=0.2 "this is important"
2/5=0.4
3/5=0.6
4/5=0.8

4) The prime number 7 has recurring digits and so have all prime number  7 and above,

This needed to be looked at...
1/7=0.142857,142857
2/7=0.285714,285714
3/7=0.428571,428571
4/7=0.571428,571428
5/7=0.714285,714285
6/7=0.857142,857142

UPDATE February 2004, I have now added a recurring digit calculator that can test for prime. 

• Remember that everything has an equal opposite or must add up to zero with any recurring digits there is always a bit missing.

• First look at prime number 7 you can see that no mater what number you divide it by, it has the same digits but rotated to a different place. Is this true with all prime numbers ( no test prime number 11 ) but they are the multiple of the same faction add together and they can be at a different but equal opposite multiples, from this it would be possible to work out any prime number from the sequence of recurring digits. do this add up

• If you divide a prime number by an even number then it will end up with an even number within it's sequence, As the second recurring number must start with the same recurring number or it would not be a recurring number. this adds up

• The number of recurring digits is 1 less then the prime number, that is prime number 7 has 6 recurring digits, this needed to be looked at is it true with all prime numbers. ( no test prime number 11 ) but I found that they are equal to prime number-1 /n The next thing is if you take half of the recurring digits and add them to the other half of the recurring digits they will add up to .9, recurring is this true with any other recurring numbers ( I found that all recurring numbers are connected with prime numbers but they may have a digit shifted and that only prime numbers add up to .9 recurring ) this add up

  • note. So at the end of the digit sequence you will end with what you started with and then you start again. This can happen with non prime number too but with a digit shifted and at some point all digits will balance.

• At this point my little desk calculator was not so handy so I made a 10,000 digit calculator, thinking that it will give me all that I wanted, but when I tested prime number 10007 I could not find the recurring digits. At this point I did not know that recurring digits could go up to a maximum of prime number -1, so I set the calculator up for 200,000 digits and found the recurring digits at 10006 digits long... and then tested prime number 100,019 with 100,018 recurring digits long...

  • I have put those recurring digits in a text document for you to look at.

I'm now working with 8,000,000 digits calculator...
 Your calculator will most likely only have 8 digits.

• I played with these numbers for about 3 days and found that each new prime number just give me a new set of the same digits but shifted and added together. So the only way they would help anyone is if the prime number or part of the prime number fitted the data, And this could be done by the equation ( start digit / prime * number of digits ) if you use more then one prime number you can get some great sequences, But sequence data is not what I'm looking for now, I revised some prime numbers so that I could understand how to roll them backup, then tried to do the same by condition the data with a feed back from the sum. But you end up with just a prime number..

END of DAY

• What I am calling these primes are route primes as they are the prime numbers that are the nearest to Sq(n) at the top of there magnitude. And proofs that prime numbers must be Infinite using the formula Prime^2^n-1,,,

  • 2^2-1 = 3 = 2^3-1 =

  • 2^2-1^2-1 = 7 = 2^7-1 =

  • 2^2-1^2-1^2-1 = 127 = 2^127-1 =

  • 2^2-1^2-1^2-1^2-1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 =

  • 2^170,141,183,460,469,231,731,687,303,715,884,105,727-1 =

  • 2^2-1^2-1^2-1^2-1^2-1,,,

• If all nonprime are multiples of primes then a root prime leys between the Sq(Pm) and Sq(Pm) – 2 which would be the prime nearest to Sq(P(m-1)) * 2 so as it is, no prime can be prime *2 - 1 making Sq(Pm)-1 must be prime.

• Back to where I started. I hadn't found what I was looking for, but I have found out lots about prime numbers. I don't think that we will ever be able to do data compression from 1 megabyte down to 1k byte.. But if you don't try you will never know, we will see....?

Update March 2004 had time to make a prime picture it holds all the prime number from 2 to 480,000

• March 2003 I have a new idea and going to find some time very soon so watch this space. I'm looking at making a 2 gigabyte digit calculator to help my next try.

  • Life is full of mistakes, that's why there are so many life species.

You can now download the prime number generator
and prime picture.

By Paul Davey copyright © 1st Nov. 2000

Since I done this, I have now seen many new websites explaining how this works.