|Themes > Science > Mathematics > Odds Ends > Unproved Theorems|
zeta(s) = 1/1s + 1/2s + 1/3s + ... (s = a + it) all 0's of zeta(s) in strip 0<=a<=1 lie on central line a=1/2
Twin Primes occur infinitely
Twin primes are primes that are 2 integers apart. Exaples include 5 & 7, 17 & 19, 101 & 103
Every even # > 2 can be expressed as the sum of 2 primes.
Euclid's Parallel Postulate
Through a point, not on a line, there exists exactly 1 line parallel to the given line. (Then there's those non-euclidean people...)
(k=1..) 1/kn = ?
Although others have found that this expression equals PI2 / 6 when n=2, PI4 / 90 when n = 4 and simular solutions for all possible even values of n, no one has discovered an exact value when n is an odd integer (3, 5, 7, ...) (note: when n=1, the sum does not converge, but it does has relations to the gamma constant).