Goldbach's weak conjecture
Goldbach's weak conjecture states that:
- Every odd number greater than 7 can be expressed as the sum of three odd primes. You are permitted to use the same prime more than once in the same sum.
This conjecture has not yet been proved, but there have been some helpful near misses. In 1937, a Russian mathematician, Ivan Vinogradov proved that all "sufficiently large" odd numbers can be expressed as the sum of three primes. Although Vinogradov was unable to say what "sufficiently large" actually meant, his own student K. Borodzin proved that 314,348,907 is an upper bound. This number has more than six million digits, so checking every number under this figure would be impossible. Fortunately, in 1989 Wang and Chen lowered this upper bound to 1043,000. If every single odd number less than 1043,000 is shown to be the sum of three odd primes, the weak Goldbach conjecture is effectively proved! However, the exponent still needs to be reduced a good deal before it is possible to simply check every single number.
See also: