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 can be represented as a sum so that both and are primes.
  • Twin prime Conjecture: There is an infinite number of pairs of the form , where both and are primes. Terence Tao video
  • Legendre’s Conjecture: There is always a prime between numbers and , where is any positive integer.

Other Conjectures

Euler’s Conjecture: The equation has no solution when are positive integers.