Conjecture

A conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.

Prime Number Conjectures:

• Goldbach’s Conjecture: Each even integer $n>2$ can be represented as a sum $n=a+b$ so that both $a$ and $b$ are primes.
• Twin prime Conjecture: There is an infinite number of pairs of the form $p,p+2$, where both $p$ and $p+2$ are primes. → Terence Tao video
• Legendre’s Conjecture: There is always a prime between numbers $n^2$ and $(n+1{)}^2$ , where $n$ is any positive integer.

Other Conjectures

Euler’s Conjecture: The equation $a^4+b^4+c^4=d^4$ has no solution when $a,b,c,d$ are positive integers.