- A beautifull day

Do you know whether there exists a fermat pseudoprime of the form

p:=n^2+n+1

By the way i started a small collection of 1000 digit primes of this form, only for your pleasure :-)

http://beablue.selfip.net/devalco/Collection/

There are approximately 2000 definitiv primes checked by pfgw in the database

Nice greetings from the primes

Bernhard - --- In primenumbers@yahoogroups.com,

"bhelmes_1" <bhelmes@...> wrote:

> Do you know whether there exists a fermat pseudoprime of the form

Yes. These [n, p] pairs make

> p:=n^2+n+1

p = n^2 + n + 1

a Carmichael number:

[2304, 5310721]

[47735, 2278677961]

[97944, 9593125081]

[172799, 29859667201]

[683808255, 467593730289953281]

David - --- In primenumbers@yahoogroups.com,

"bhelmes_1" <bhelmes@...> wrote:

> p:=n^2+n+1

...

> i started a small collection of 1000 digit primes of this form

The Prime Pages list 1357 primes of this form:

> Used 1.2427 second(s) to find

The largest has 208601 digits and was found by PrimeMogul himself:

> 1357 primes matching the selection criteria:

> Description must match: Phi\\(3,.*\\)$.

http://primes.utm.edu/primes/page.php?id=83711

David