mrBlah said: “What about 1 not actually being prime, but special. A prime is divisible by itself and 1 only; two numbers. The number 1 is only divisible by itself; only one number.”

It took eight and a half years but here it is….finally.

That’s why 1 is the loneliest number.

Back in March of 2000 a group of London publishers were offering the equivalent of 1.5 million Canadian dollars to anyone who could prove the theory that all even numbers greater than 4 were the sum of 2 prime numbers. Prime numbers for those not knowing is a number that is only divisible evenly by itself and one (examples are 1, 3, 5, 7, 11, 13, etc.). So for example, the even number 16 according to Goldbach would be the result of adding the two prime numbers 3 and 13. They gave participants until March 15, 2002 to come up with a solution. The publishers were not in the least bit worried about having to pay it out and they didn’t.
This puzzle is known as Goldbach’s first conjecture and was first raised by the Prussian mathematician, Christian Goldbach way back in the year 1742. It was discovered in correspondence between Christan Goldback and another mathematician by the name of Leonhard Euler from Switzerland. According to all accounts this theory has not been proven in the past 263 years but has been verified up to 4×10 to the 14 power by using an optimized segmented sieve and an efficient checking algorithm. Enough already!
It is easy to think of any even number and come up with 2 prime numbers that when added together total that even number. The problem though is trying to prove that it works for every even number imaginable. Now you know my dilemma so don’t get me started on Goldbach’s other conjecture! What is Goldbach’s other conjecture you ask? Check it out for yourself at the link below: http://www.andrews.edu/~calkins/math/biograph/biogoldb.htm Now, sorry you asked?”

I also work on Goldbach’s Conjecture. I would like to point out that the other conjecture is nothing more than a rewording of the 2 primes conjecture. If one has 3 primes, the sum of two of them are an even number by the primary conjecture. This means an odd (prime) and an even number equal an odd number. What this means is that we can take an arbitary prime (eg 3) and then using the primary conjecture create any odd number by selecting the correct two primes to create the requisite even number.
There is only one conjecture. The real answer to the conjecture is to prove that the prime numbers are clustered close enough together such that they can cover the binary partition of all even numbers less than double the largest odd prime.”[/quote]

i solved the problems you were looking at it was relativley easy

I agree with you one hundred percent haha

This depends on the size of the key. It used to be that 1024 or 2048 was considered strong. Now techniques are in use that allow cracking 2048 keys in reasonable amounts of time. At the current time a key length of less than 4096 is probably only moderately strong. And I expect that key length to crack in 2-3 years. There was an announcement today for example about two new quantum computing chips that were released. Once this technology comes to market about 2015 RSA, knapsack, and similar algorithms based on modulo and prime factoring will no longer be usable.