http://www.mathisfunforum.com/viewtopic.php?id=20868

The most amazing things about it, were all personal. I became further convinced that EM was the only way to go if one desired to get the right answer an infuriating amount of times. Also, we were 2 of only 4 people in the world who knew that those Stanford and Duke university guys were not arguing with Marilyn. That would have been difficult enough, they were arguing with their own methods and colleagues who had hashed this problem to death in a statistics journal, many years before. RIPOSTP.

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]]>I am a guy who came into this forum in 2009. I currently live in the badlands of Florida.

did you become administrator

In March of 1990 at the tender age of 70 I decided to devote most of my remaining brain cells to mathematics. This was primarily the result of a dare by people who believed that I was a loser and could not stick to anything for more than a short time. They were partially right but I could stick to something if I wanted to. So, in that month I decided that I would teach myself mathematics and computers full time. I also made the promise that at the end of 20 years if I could not do any real math, I would quit forever. In April of 2009 ( the 19th year ) I decided it was time to see if I had succeeded.

I noticed the MathsisFun forum and one character in particular, the legendary JaneFairfax. She seemed to be the best problem solver on the forum and naturally I wanted to see how I would do against the best they had.

I did not do anything that I considered amazing for the first couple of weeks until the tongzilla problem appeared. When I solved that one, I knew I had succeeded. I had learned mathematics using my own methods and my own ideas. I had discovered EM. Naturally, my original detractors suddenly forgot their accusations but I did not.

Then I had to calm my mind so that I would not forget that what I had done was not amazing, it was not even difficult. To do that I used the techniques that pappym taught me from your country. They were much harder than mathematics and I am still working on them.

Why am I an administrator? Beats me...only MIF can answer that question. But it has been a privilege to serve here and to know the people that are here. A privilege I do not deserve but have been given to me anyway.

]]>1,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192..........

which is nothing but powers of 2.So,it is actually

2^0,2^0,2^1,2^2,2^3,2^4,2^5,2^6.........

Using the solutions of the equation Pell.

Solution write.

]]>There is also a formula first noticed by Leonhard Euler which proves that the set of primes is endless. The formula is

x²+x+41 is always a prime no. if x is an integer.

This cannot be true: just take x = 41 for instance, which clearly factorises into non-trivial factors. Euler found that this polynomial produces 40 distinct primes for the first 40 values.

In fact, it can be shown that such a polynomial cannot exist.

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Ps=77777777777777777777777777777777813

I knew it all along. Can you imagine that if we shuffled up all possible axiomatic systems and picked one at random we would probably have a better formal system than logic?! That math itself, is nothing more than the hidden rule of saying to oneself, hey, let us find something trivial, that we think is pretty and see if we can find some theorems about it. Does this mean it is kaboobly doo? The queen of science and the epitome of human thought is kaboobly doo?

Who would say such a thing? Myself? I just learned last month that for 92 years I have been tying my shoes the wrong way! Obviously, bumpkins are not bright enough to hold such an opinion. Doron maybe? Nope, it would have to be a super genius. More importantly, it would have to be someone who could say such a thing.

]]>Bonus points if you can prove it without the use of a computer or wolfram alpha!

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Not a chance, formalism is more akin to my beliefs.

Robert Burns wrote:

Is there for honest Poverty

That hings his head, an' a' that;

The coward slave - we pass him by,

We dare be poor for a' that!

For a' that, an' a' that.

Our toils obscure an' a' that,

The rank is but the guinea's stamp,

The Man's the gowd for a' that.What though on hamely fare we dine,

Wear hoddin grey, an' a that;

Gie fools their silks, and knaves their wine;

A Man's a Man for a' that:

For a' that, and a' that,

Their tinsel show, an' a' that;

The honest man, tho' e'er sae poor,

Is king o' men for a' that.Ye see yon birkie ca'd a lord,

Wha struts, an' stares, an' a' that,

Tho' hundreds worship at his word,

He's but a coof for a' that.

For a' that, an' a' that,

His ribband, star, an' a' that,

The man o' independent mind,

He looks an' laughs at a' that.A Prince can mak a belted knight,

A marquis, duke, an' a' that!

But an honest man's aboon his might –

Guid faith, he mauna fa' that!

For a' that, an' a' that,

Their dignities, an' a' that,

The pith o' Sense an' pride o' Worth

Are higher rank than a' that.Then let us pray that come it may,

As come it will for a' that,

That Sense and Worth, o'er a' the earth

Shall bear the gree an' a' that.

For a' that, an' a' that,

It's comin yet for a' that,

That Man to Man the warld o'er

Shall brithers be for a' that.

And some art...

I did like the part about the lemurs being about as good as those humans at math. I also enjoyed seeing Maria, I had no idea she was a woman.

A man's a man for a' that

and a' that and a' that

This is a bias and they discovered biases for prime numbers ending in 3,7 and 9 as well.

Chebyshev's bias tends to correct itself asymptotically.

]]>I get the beginning but not the end of it where you've put (-1/p)=-1.

Let's define the quadratic residue symbol.

First of all, suppose is an odd prime, and let be a non-zero number coprime to Then, is called a quadratic residue modulo if the congruence has solutions. If it doesn't, then we say that is called a quadratic non-residue. The quadratic residue symbol summarises this information. We define:So if I say that whenever , that just means the congruence has no solutions for such primesPrimenumbers wrote:

What I'm saying is that primes less than a given number say, are more likely to be than they are But primes congruent to don't appear in your factorisation of anyway -- so this tells us that slightly more than 50% of primes will never appear in your factorisation, which is due to Chebyshev's bias. But as they approach the same value.]]>First point is correct but I just wanted to show that by using

we can reduce the number of possible factors which should help compute primes faster. And now you have shown that will never be factorable by the primes of the form so thank you. I thought about 50% of primes could not possibly be factors but now you're saying that not only would there be 50%, but that there would be a bias to more than 50% due to Chebyshev's bias. Have I got this right?I am also still trying to work out if there's anything else we can use this scenario for to do with primes. If there was a wheel of prime factors that could factor

, it would be 20m + 1 or 9 or 13 or 17, not including 2 and 5.

I'm not sure but I'm guessing this would be a faster way to compute finding primes. I.e. using Euclid's algorithm.

See............https://en.wikipedia.org/wiki/Euclidean_algorithm

Primality Tests are usually done on numbers in the range of 2^1024 to 2^2048 (or much, much bigger numbers, when it's simply about "finding a prime", not crypto). Enumerating (and multiplying!) all the primes below those numbers is an insurmountable task.

If enumerating all primes was easy, RSA would be useless :-p

Edit: I just saw this thread is kinda old (still first page), I hope this doesn't count as necromancy

]]>Incidentally, do not use the short form of this games name in your post or the server will bar you.

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