What a

There appears to be some discouragement in the mathematics community

at ever being able to come to grips with the Goldbach conjecture, in particular

with the notion that any even whole number can be expressed as the sum of

a mere two prime numbers. Here are my musings on the subject.

The Goldbach conjecture states that every even whole number can be expressed

as the sum of two prime numbers. I would break this down to mean that any

even whole number has at least one such solution : our little friend 8 is the sum

of 3 and 5. 80 is the sum of 3 and 77, but also that of 27 and 53.

My concern, qua translator of German to English, though, would be to convey

that he says that every even integer is a thus sum, and not any even integer; i.e.

we are not in a gambler’s realm of unpredictables and Herr Goldbach is placing a bet, 

but rather the number system is ordered and we can generalize about it.

Consider the following example with 40 as the ‘begin’ even integer. It can be expressed

as the sum of the two prime numbers 17 and 23. Its successor even integer 42,

in turn, is the sum of the prior and successor primes 13 and 29 and so forth.

One needs to be careful, though, with 19 which pairs with non-prime 21 to give 40.

Notice, however, that 19 pairs with itself to give 38, the prior whole integer, not part of

the Goldbach but in the series nonetheless.

Setting ‘begin’ at 80, the nearest-to-half prime pairs with another prime: 37 pairs with

43 to yield 80. Have a chuckle: 37 goes with 3 to yield 40.

The point to the whole exercise is that each even integer is unique and will, like the

cases of the old Naked City television program, have its own story.