### Saturday, October 31, 2009

## JSH: Prime distribution and Occam's Razor

I discovered back in 2002 a rather simple formula for counting prime numbers.

That formula has several unique features while it is also very similar in key ways to what was previously known.

One of those unique features is a difference equation form which leads to a partial differential equation.

That is important as for some time mathematicians have known about a connection between the count of prime numbers and various continuous functions where for simplicity I give x/ln x as that is easily checkable at your computer.

For instance there are 4 primes up to 10: 2, 3, 5 and 7. While 10/ln 10 = 4.3 to one significant digit.

And one more example to give a better sense of it, consider 100, as there are 25 primes up to 100, while 100/ln 100 = 21.7 to one significant digit.

Notice though there is a gap, as 21.7 is much further from 25 than 4.3 was from 4, and my research can explain that gap simply enough.

(One area where my research contradicts with established theory as by that theory the gap will eventually shrink and even reverse! My research indicates it will not, but steadily grows bigger out to infinity.)

There is a lot of competing mathematics in this area. Mathematicians have done a lot of research on prime numbers and introduced some extraordinarily advanced tools for their study. But I made a stunningly simple discovery which allows an alternate explanation for some of the why's of the prime distribution which they have deliberately ignored.

I can say they've deliberately ignored it as I did send the result to top mathematicians almost immediately upon its discovery back in 2002, and have sent it to mathematicians all over the world and tried to get it published, to no avail.

Occam's Razor applies as you have a simple explanation for why the prime counting function is close to x/ln x, with a simple explanation for the gap between that value and the prime count, which follows just from knowing that a mathematical formula that counts primes leads to this partial differential equation.

It's impossible to justify simply ignoring the result. And worse, leaving its discoverer out as a "crackpot" to be insulted is very unethical behavior on the part of mathematicians. There simply is no way to justify such acts.

However such behavior is consistent with a willful desire to hold on to the more abstruse results rather than deal with an extreme simplification.

Physicists may love simplifications but mathematicians pride themselves on building what came before, and claim few upheavals in their field.

They love complexity, and pride themselves on difficult mathematical ideas which few people understand. My result ruins the prime distribution from that perspective by giving a simple and possibly too mundane explanation for people who love difficulty, and pride themselves on complexity.

Regardless of what you believe, you probably realize that if mathematicians simply refused to acknowledge a major result it could be extremely difficult for that result to become widely known.

And you must realize then that they are themselves so aware.

That formula has several unique features while it is also very similar in key ways to what was previously known.

One of those unique features is a difference equation form which leads to a partial differential equation.

That is important as for some time mathematicians have known about a connection between the count of prime numbers and various continuous functions where for simplicity I give x/ln x as that is easily checkable at your computer.

For instance there are 4 primes up to 10: 2, 3, 5 and 7. While 10/ln 10 = 4.3 to one significant digit.

And one more example to give a better sense of it, consider 100, as there are 25 primes up to 100, while 100/ln 100 = 21.7 to one significant digit.

Notice though there is a gap, as 21.7 is much further from 25 than 4.3 was from 4, and my research can explain that gap simply enough.

(One area where my research contradicts with established theory as by that theory the gap will eventually shrink and even reverse! My research indicates it will not, but steadily grows bigger out to infinity.)

There is a lot of competing mathematics in this area. Mathematicians have done a lot of research on prime numbers and introduced some extraordinarily advanced tools for their study. But I made a stunningly simple discovery which allows an alternate explanation for some of the why's of the prime distribution which they have deliberately ignored.

I can say they've deliberately ignored it as I did send the result to top mathematicians almost immediately upon its discovery back in 2002, and have sent it to mathematicians all over the world and tried to get it published, to no avail.

Occam's Razor applies as you have a simple explanation for why the prime counting function is close to x/ln x, with a simple explanation for the gap between that value and the prime count, which follows just from knowing that a mathematical formula that counts primes leads to this partial differential equation.

It's impossible to justify simply ignoring the result. And worse, leaving its discoverer out as a "crackpot" to be insulted is very unethical behavior on the part of mathematicians. There simply is no way to justify such acts.

However such behavior is consistent with a willful desire to hold on to the more abstruse results rather than deal with an extreme simplification.

Physicists may love simplifications but mathematicians pride themselves on building what came before, and claim few upheavals in their field.

They love complexity, and pride themselves on difficult mathematical ideas which few people understand. My result ruins the prime distribution from that perspective by giving a simple and possibly too mundane explanation for people who love difficulty, and pride themselves on complexity.

Regardless of what you believe, you probably realize that if mathematicians simply refused to acknowledge a major result it could be extremely difficult for that result to become widely known.

And you must realize then that they are themselves so aware.