# 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:

**Goldbachâ€™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. â†’ Terence Tao video**Legendreâ€™s Conjecture**: There is always a prime between numbers $n_{2}$ and $(n+1)_{2}$ , where $n$ is any positive integer.

### Other Conjectures

Eulerâ€™s Conjecture: The equation $a_{4}+b_{4}+c_{4}=d_{4}$ has no solution when $a,b,c,d$ are positive integers.