Goldbach's Conjecture

Goldbach's Conjecture is one of the oldest unsolved problems in number theory. It states the following

Every even integer greater than 2 can be expressed as the sum of two prime numbers.

For Example:

• 4 = 2 + 2
• 6 = 3 + 3
• 8 = 3 + 5
• 10 = 5 + 5 or 7 + 3

Interesting Facts about Goldbach's Conjecture

Some interesting facts about Goldbach's Conjecture are:

• Binary or Strong Goldbach's Conjecture: Every even number > 2 is the sum of two Primes.
• Ternary or Weak Goldbach's Conjecture: Every odd number > 5 can be written as the sum of three Prime Numbers.
• A stronger version of the weak conjecture, namely that every odd number ≥ 7 can be expressed as the sum of a prime plus twice a prime is known as Levy's conjecture (where ϕ(x) is the totient function).
• Some mathematicians explore whether every even integer greater than 4 can be written as the sum of two distinct odd primes, adding a bit more complexity to the original conjecture.
• The conjecture has been confirmed to be true for all numbers smaller than 4×10¹⁸, but no one has been able to prove it completely, despite a lot of effort.

Note: The weak conjecture was proven in 2013 by mathematician Harald Helfgott.

Read More,

• Prime Numbers
• Composite Numbers
• Interesting Facts About Prime Numbers