## fermat pseudoprimes p=n^2+n+1

Expand Messages
• 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
Message 1 of 3 , Jul 10, 2010
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
• ... Yes. These [n, p] pairs make p = n^2 + n + 1 a Carmichael number: [2304, 5310721] [47735, 2278677961] [97944, 9593125081] [172799, 29859667201] [683808255,
Message 2 of 3 , Jul 10, 2010
"bhelmes_1" <bhelmes@...> wrote:

> Do you know whether there exists a fermat pseudoprime of the form
> p:=n^2+n+1

Yes. These [n, p] pairs make
p = n^2 + n + 1
a Carmichael number:

[2304, 5310721]
[47735, 2278677961]
[97944, 9593125081]
[172799, 29859667201]
[683808255, 467593730289953281]

David
• ... The largest has 208601 digits and was found by PrimeMogul himself: http://primes.utm.edu/primes/page.php?id=83711 David
Message 3 of 3 , Jul 10, 2010
"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
> 1357 primes matching the selection criteria:
> Description must match: Phi\\(3,.*\\)\$.

The largest has 208601 digits and was found by PrimeMogul himself:
http://primes.utm.edu/primes/page.php?id=83711

David
Your message has been successfully submitted and would be delivered to recipients shortly.