mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2007-10-10, 00:37   #1
Carl Fischbach
 
Carl Fischbach's Avatar
 
Oct 2007

2×17 Posts
Default An equation to generate all primes that uses 2 & 3

I've come up with this equation after working a long time with primes.

PRIME GENERATOR


A +/- B= prime


ex (2*3*5*7-11*13)=67

The numbers on the left are a series of all prime starting with 2 that go up
any prime value in this case is 13 and any prime can appear more than
once provided it only appears on one side fo the addition or subtraction.
the other condition is that the number it produces in this case is 67
is always prime if (max. prime on left)^2 is greater than the number on the right. In this case 13^2 is greater than 67 therefore 67 is prime.
Note the primes on the left can contain a larger prime not in sequence as in the example (3*5*7-2*29)=47 provided (max prime of sequence)^2 is
greater than the number on the right. In this case 7^2 is greater than
47.


THE PROOF

The proof as why the number on the right is always prime is because
it has a minimum of 2 potential factors if not prime. The primes on the left are present at least once in all the potential factor possibilities of the
number on the right.
Now if you factor out any potential odd factors from the primes on the
left you now have a whole number on one side of the addition or subtraction and a nonwhole on the other side of the addition or subtraction, which gives you a nonwhole in the brackets on the left.
You now have a nonwhole as a factor for every potential factor
of the number on the right so therefore the number on the right must
be prime.


THE FISCHBACH CONJECTURE


The Fischbach conjecture says that all primes can be generated by starting with 2 and 3 in the above equation and use the generated primes to further generate all possible primes.




Here are the first 14 primes generated from 2 and 3

2+3=5
2*2+3=7
2*5+3=13
3*5+2=17
2*2*2*3-5=19
2*3*5-7=23
7*5-2*3=29
5*3*3-2*7=31
5*3*2+7=37
5*7+2*3=41
2*5*7-3*3*3=43
3*5*7-2*29=47
Carl Fischbach is offline   Reply With Quote
Old 2007-10-10, 02:14   #2
Mini-Geek
Account Deleted
 
Mini-Geek's Avatar
 
"Tim Sorbera"
Aug 2006
San Antonio, TX USA

22·11·97 Posts
Default

Quote:
Originally Posted by Carl Fischbach View Post
ex (2*3*5*7-11*13)=67

The numbers on the left are a series of all prime starting with 2 that go up
any prime value in this case is 13 and any prime can appear more than
once provided it only appears on one side fo the addition or subtraction.
the other condition is that the number it produces in this case is 67
is always prime if (max. prime on left)^2 is greater than the number on the right. In this case 13^2 is greater than 67 therefore 67 is prime.
Note the primes on the left can contain a larger prime not in sequence as in the example (3*5*7-2*29)=47 provided (max prime of sequence)^2 is
greater than the number on the right. In this case 7^2 is greater than
47.
How do you come up with the numbers on the right? How I understand it, (2*3*5*7)-(2*2*2*5*5)=10 (parentheses for clarity) should be prime, since 72=49 is more than 10. 10 is obviously not prime, so either I am misunderstanding your conjecture, it is incorrect, or both.
Mini-Geek is offline   Reply With Quote
Old 2007-10-10, 02:39   #3
Carl Fischbach
 
Carl Fischbach's Avatar
 
Oct 2007

2·17 Posts
Default clarifying equation

In the example you have illustrated you have 2 and 5 on both sides
of the minus sign. In the defintion of the equation you can have one value
of prime on only one side of the minus sign not on both. To change
your example bit 2*2*2*5-3*7=19 which is prime.
Carl Fischbach is offline   Reply With Quote
Old 2007-10-10, 03:52   #4
bsquared
 
bsquared's Avatar
 
"Ben"
Feb 2007

1101111110102 Posts
Default

Quote:
Originally Posted by Carl Fischbach View Post
...
THE FISCHBACH CONJECTURE


The Fischbach conjecture says that all primes can be generated by starting with 2 and 3 in the above equation and use the generated primes to further generate all possible primes.

...
Generate M45 for me and I'll say you have something...
bsquared is offline   Reply With Quote
Old 2007-10-10, 04:13   #5
Carl Fischbach
 
Carl Fischbach's Avatar
 
Oct 2007

428 Posts
Default unlimited computer power

When they develope unlimited computer power I"ll generate M45 with
this algorithm.
Carl Fischbach is offline   Reply With Quote
Old 2007-10-10, 05:03   #6
Carl Fischbach
 
Carl Fischbach's Avatar
 
Oct 2007

2×17 Posts
Default primes may run out

A lot of people on this forum are after the largest prime, I've got news for you, primes being a digital occurence can not be analysed with analog
equations as to if primes continue for infinity. I've developed a digital
analysing system that tells you the exact number of primes from 0 to any number I've yet to finalize all the equations to come up with an exact
number primes,it requires a lot of work and I don't have the time for it right now, but early results so that primes may run out, so maybe these
searches are a waste of time.
Carl Fischbach is offline   Reply With Quote
Old 2007-10-10, 06:04   #7
bsquared
 
bsquared's Avatar
 
"Ben"
Feb 2007

1101111110102 Posts
Default

Quote:
Originally Posted by Carl Fischbach View Post
When they develope unlimited computer power I"ll generate M45 with
this algorithm.
What algorithm? I haven't seen anything that tells me systematically how to pick the primes on the left, or where to put the +/-, other than possibly trial and error. In less than a second, I found 1000099999 to be prime using the sieve of erathosthenes. What is your formula for that?
bsquared is offline   Reply With Quote
Old 2007-10-10, 11:42   #8
Mr. P-1
 
Mr. P-1's Avatar
 
Jun 2003

7×167 Posts
Default

Quote:
Originally Posted by Carl Fischbach View Post
The numbers on the left are a series of all prime starting with 2 that go up
any prime value...

[...]

3*5*7-2*29=47
This formula does not satisfy the "sequence" as you have defined it, as it contains 29 but does not contain all primes up to 29.
Mr. P-1 is offline   Reply With Quote
Old 2007-10-10, 12:03   #9
Mini-Geek
Account Deleted
 
Mini-Geek's Avatar
 
"Tim Sorbera"
Aug 2006
San Antonio, TX USA

10AC16 Posts
Default

Quote:
Originally Posted by Carl Fischbach View Post
A lot of people on this forum are after the largest prime, I've got news for you, primes being a digital occurence can not be analysed with analog
equations as to if primes continue for infinity. I've developed a digital
analysing system that tells you the exact number of primes from 0 to any number I've yet to finalize all the equations to come up with an exact
number primes,it requires a lot of work and I don't have the time for it right now, but early results so that primes may run out, so maybe these
searches are a waste of time.
I'm not quite sure what you're trying to get at by the difference between digital and analog things, but primes are infinite, and we aren't searching for "the largest prime", we're searching for ever larger prime, which are known as "the largest known prime" when they're discovered. Whether or not there are infinite Mersenne Primes is not known.
Proof of infinite primes: http://en.wikipedia.org/wiki/Prime_n..._prime_numbers
Basically, what it's saying is that if you take a set of primes (e.g. {2,3,5}), multiply them together and add 1 (e.g. 2*3*5+1=31) the resulting number is either prime (as with 31), or divisible by primes not in the original set (as with 3*5+1=16=24), meaning there is always another prime number.
Quote:
Originally Posted by Carl Fischbach View Post
In the example you have illustrated you have 2 and 5 on both sides
of the minus sign. In the defintion of the equation you can have one value
of prime on only one side of the minus sign not on both. To change
your example bit 2*2*2*5-3*7=19 which is prime.
Oh, ok, I didn't understand that the same prime value can't be used in both sides. I'll keep trying to look for a counter-example, as this would seem to be the easiest way to prove this conjecture wrong (don't want to seem as if I'm just trying to say you're wrong, but finding a counter-example would seem to be the easiest way to prove or disprove this)
EDIT: I think I found one. 211*223-199=46854=2 x 3 ^ 2 x 19 x 137. 2232=49729 which is higher than 46854. Also, 199, 211, and 223 are consecutive primes.

Last fiddled with by Mini-Geek on 2007-10-10 at 12:15
Mini-Geek is offline   Reply With Quote
Old 2007-10-10, 13:01   #10
Carl Fischbach
 
Carl Fischbach's Avatar
 
Oct 2007

2×17 Posts
Default To clarify my definition

The equation can contain any prime but it must contain a sequence of
primes from 2 to the prime just greater than ( the number generated)^.5
and if this condition is satisfied then the number generated is prime.
Carl Fischbach is offline   Reply With Quote
Old 2007-10-10, 13:10   #11
Carl Fischbach
 
Carl Fischbach's Avatar
 
Oct 2007

1000102 Posts
Default The algorithm

This is a prime generator not a prime tester. You have to randomly
arrange known primes in the equation to generate larger primes from
the equation.
Carl Fischbach is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Titan V may generate false results. MisterBitcoin GPU Computing 28 2018-05-04 18:11
Generate Unrestricted Grammars Raman Puzzles 3 2013-09-15 09:15
New(?) Algorithm to Generate Cycles russellharper Factoring 10 2010-12-01 01:33
Have Found Principle to generate infinitive PRIME NUMBERS Evgeny Dolgov Miscellaneous Math 38 2010-09-05 17:45
Effective way to generate prime numbers (infinitive) Evgeny Dolgov Math 1 2003-12-08 09:25

All times are UTC. The time now is 10:13.


Sat Oct 16 10:13:44 UTC 2021 up 85 days, 4:42, 0 users, load averages: 0.87, 1.14, 1.05

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.