Here we state a theorem that finds composite numbers. Proof will be given elsewhere. Theorem: Let $latex A = \{ a: 1\leq a\leq N\}$ and $latex B = \{b: 1\leq b\leq N\}$ Define $latex x =\frac{a+b+1+\sqrt((a-b)^2+2a+2b+5)}{2}$ for $latex a$ in $latex A$ and $latex b$ in $latex B$. If $latex x\in \mathbb{N}$, then $latex x+1$... Continue Reading →
A New Method of Factoring Large Integers
Abstract In this paper, we reduce a large integer $latex N$ to an integer $latex N^\prime$, which has a smaller number of decimal digits than $latex N$. Then we find the greatest common divisor (gcd) of $latex N$ and $latex N^\prime$ to return a nontrivial factor of $latex N$. Introduction The branch of mathematics that... Continue Reading →
Goldbach Conjecture
According to Golbach's conjecture, every even greater than 2 is the sum of two primes. Here we experimentally demonstrate that it is only true if there are infinitely many primes. Theorem: There are infinitely many primes. Proof: We prove this using Goldbach conjecture. Suppose a finite set of prime numbers P = {p1, p2, …,... Continue Reading →
Does God Exist? Simple Answer of the Difficult Question
Let us settle this difficult question once and for all. Perhaps we would never be able to prove the existence of God as any proof would involve the underlying assumptions. The same goes for disproof. A mathematical proof may be possible. But physical evidences are not guaranteed. However, if we change the question and ask,... Continue Reading →
Mr. Monologue 