I'm not entirely sure what you mean by the Fermat 4n+1 theorem and

the Euler 6n+1 theorem. Could you explain this please?

Whatever it is, I'd like to see the proof myself!

Mark

PS Regarding my previous post on prime twins separated by 30 and 210,

it turns out that latter is about 1.44 times as abundant as the

former. So my heuristic estimate of 1.33 is somehow faulty.

Checking twins up to 60000000 gives counts of 12701 and 18302,

yielding a ratio of about 1.44

Mark

--- In

primenumbers@yahoogroups.com, najiba amimar

<najibaamimar@y...> wrote:

> Hi all!

>

> Can someone give me the proof of fermat 4n+1 theorem

> and euler 6n+1 theorem? These two theorem are found

> very commonly on web pages, but never with the proof.

>

> These two theorem are result of diophantine equation

> of SECOND order. Is anyone know if it exist solutions

> for an higher order for a representation of a prime

> number?

>

> Thanks a lot

>