 mersenneforum.org An equation to generate all primes that uses 2 & 3
 Register FAQ Search Today's Posts Mark Forums Read  2007-10-10, 00:37 #1 Carl Fischbach   Oct 2007 2×17 Posts 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   2007-10-10, 02:14   #2
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

22·11·97 Posts Quote:
 Originally Posted by Carl Fischbach 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.   2007-10-10, 02:39 #3 Carl Fischbach   Oct 2007 2·17 Posts 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.   2007-10-10, 03:52   #4
bsquared

"Ben"
Feb 2007

1101111110102 Posts Quote:
 Originally Posted by Carl Fischbach ... 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...   2007-10-10, 04:13 #5 Carl Fischbach   Oct 2007 428 Posts unlimited computer power When they develope unlimited computer power I"ll generate M45 with this algorithm.   2007-10-10, 05:03 #6 Carl Fischbach   Oct 2007 2×17 Posts 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.   2007-10-10, 06:04   #7
bsquared

"Ben"
Feb 2007

1101111110102 Posts Quote:
 Originally Posted by Carl Fischbach 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?   2007-10-10, 11:42   #8
Mr. P-1

Jun 2003

7×167 Posts Quote:
 Originally Posted by Carl Fischbach 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.   2007-10-10, 12:03   #9
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

10AC16 Posts Quote:
 Originally Posted by Carl Fischbach 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 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   2007-10-10, 13:01 #10 Carl Fischbach   Oct 2007 2×17 Posts 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.   2007-10-10, 13:10 #11 Carl Fischbach   Oct 2007 1000102 Posts 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.   Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post MisterBitcoin GPU Computing 28 2018-05-04 18:11 Raman Puzzles 3 2013-09-15 09:15 russellharper Factoring 10 2010-12-01 01:33 Evgeny Dolgov Miscellaneous Math 38 2010-09-05 17:45 Evgeny Dolgov Math 1 2003-12-08 09:25

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