Solve the system.

The solution can be written as.

]]>A=2x3x5x7x11x13x17........ up to

m=Any multiple

A-pm= A number factorable by a factor of p

if p has one.To get A-pm, go through the primes, subtracting p as many times as you like.

Example:

p=129

A=2x3x5x7x11

2x3x5x7=210 210-129=81

81x11=891 891-(129x6)=117

A-129m=117

117 will have a factor the same as p if it has any.

117/129=39/43 129 is NOT prime (Common denominator =3)

In this way we can find out if p is composite without ever having to use a number

. Might be useful for computers.]]>Example:

p=130

Rd. Up to nearest prime= 13

Next prime after that = 17

17-1=16

Largest prime gap <130 = 16 (Correct)

This works because the greatest number of composites between two primes occurs when factors are not combined. So what could have been two composites is actually just one, like 15=3x5. To create the greatest possible number of composites I start at 2 not 0. 0 has an infinite number of prime factors, and so the greatest gap between the next repeat will occur after 0. Starting with the smallest composite which is NOT combined factors, I move up. Deleting all numbers factorable by primes less than the square root. The first time I attain TWO primes is when I reach the second prime after the square root. So this -1 is the gap required to create two non-composites with greatest possible occurrence of composites.

Largest prime gap <p =

Rd. Up to second nearest prime -1.]]>The formula is too complicated to remember. It can be remembered much more easily by Implementing Faulhaber's formula. It says,

1ˣ +2ˣ +3ˣ +4ˣ ......nˣ =[1/(1+x)](aB₀nˣ⁺¹+bB₁nˣ+cB₂nˣ⁻¹............yBₓn), where Bₙ is the nth Bernoulli no. and a,b,c,.....y are the consecutive terms of (x+1)th row of Pascal's Triangle.

For e.g.

1¹¹+2¹¹+3¹¹+4¹¹.....7¹¹=(1/12)(1B₀n¹²+12B₁n¹¹+66B₂n¹⁰+220B₃n⁹+495B₄n⁸+792B₅n⁷+924B₆n⁶+792B₇n⁵+495B₈n⁴+220B₉n³+66B₁₀n²+12B₁₁n)

(1+B)ⁿ⁺¹-Bₙ₊₁=0

For e.g.

for,B₁ n=1 so

(1+B)²-B₂=0

⇒1+B₂+2B-B₂=0

⇒1=2B=0

⇒B=-0.5

However in this ( the formula for sums of powers )formula B₂=+0.5]]>

Sorry, haven't been keeping up with the "this is cool" feed. But nice job!

]]>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.

]]>URL:http://www.mathsisfun.com/numbers/infinity.html

]]>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.........

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.

]]>p=35

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.

]]>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