Conference rusure::math

701.0. "Goldbach wasn't always right!" by AKQJ10::YARBROUGH (Why is computing so labor intensive?) Fri May 08 1987 08:48

Here are two more number-theory conjectures that you may want to 
investigate (Ain't microvaxen fun?):


1) [Goldbach, again] Every odd number is the sum of a prime and twice a 
square (0 included); e.g. 21 = 19+2, or 13+8, or 3+18.

This is known to be false, but the exceptions are few and far between.


2) Every even number is the sum of a prime and a power of an integer. E.g.
856 = 127 + 9*9*9. 

This one is undetermined. It is also true for 'most' odd integers also;
i.e., exceptions are rare.

Lynn Yarbrough