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• ## generalized fermat primes and generalized femat-proth primes

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• Hi, I recently became interested in these. generalized fermat primes(GFN) are primes of the from k^(2^n)+1 I am looking for the lowest value of k such that
Message 1 of 2 , Jun 19, 2003
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Hi,
I recently became interested in these.
generalized fermat primes(GFN) are primes of the from k^(2^n)+1
I am looking for the lowest value of k such that k^(2^n)+1
is primefor each n. I have the list upto 2048 could some one help me
complete the list to include all known generalized fermats.

2^2+1
2^4+1
2^8+1
2^16+1
30^32+1
102^64+1
120^128+1
278^256+1
46^512+1
824^1024+1
150^2048+1

generalized femat-proth primes(GFPN) are something I termed. They are
primes of the form k*2^(2^n)+1.(I don't know if there is any other
name for these type of primes.)I am looking for the lowest k such
that k*2^(2^n)+1 is prime for each value of n. I have this list
completed upto 2^13. Could some one help me finish this list to
higher values of n. (or if someone knows of any primes in this
category.)

3*2^2+1
7*2^4+1
3*2^8+1
21*2^16+1
43*2^32+1
25*2^64+1
21*2^128+1
207*2^256+1
223*2^512+1
1125*2^1024+1
2577*2^2048+1
3091*2^4096+1
9165*2^8192+1

If there are no primes known and you are interested in searching
these primes let me know so we can coordinate a team effort.
My email is harsh@...

For the GFN's there is a team effort going on at
but since they are searching for GFN in general and not for the
lowest k, you can't just join there project.
Also to search for GFN we will have to tag-team with them.

Anyway if you are intrested email me.

Thanks!
Harsh Aggarwal
• Hi, I found an updated list for the GFN on the internet. 2^2+1 2^4+1 2^8+1 2^16+1 30^32+1 102^64+1 120^128+1 278^256+1 46^512+1 824^1024+1 150^2048+1
Message 2 of 2 , Jun 19, 2003
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Hi,
I found an updated list for the GFN on the internet.
2^2+1
2^4+1
2^8+1
2^16+1
30^32+1
102^64+1
120^128+1
278^256+1
46^512+1
824^1024+1
150^2048+1
1534^4096+1
30406^8192+1
67234^16384+1
70906^32768+1
48594^65536+1
62722^131072+1*
* 62722 may not be the smallest k for 131072.

--Harsh
--- In primenumbers@yahoogroups.com, "eharsh82" <harsh@u...> wrote:
> Hi,
> I recently became interested in these.
> generalized fermat primes(GFN) are primes of the from k^(2^n)+1
> I am looking for the lowest value of k such that k^(2^n)+1
> is primefor each n. I have the list upto 2048 could some one help
me
> complete the list to include all known generalized fermats.
>
> 2^2+1
> 2^4+1
> 2^8+1
> 2^16+1
> 30^32+1
> 102^64+1
> 120^128+1
> 278^256+1
> 46^512+1
> 824^1024+1
> 150^2048+1
>
> generalized femat-proth primes(GFPN) are something I termed. They
are
> primes of the form k*2^(2^n)+1.(I don't know if there is any other
> name for these type of primes.)I am looking for the lowest k such
> that k*2^(2^n)+1 is prime for each value of n. I have this list
> completed upto 2^13. Could some one help me finish this list to
> higher values of n. (or if someone knows of any primes in this
> category.)
>
> 3*2^2+1
> 7*2^4+1
> 3*2^8+1
> 21*2^16+1
> 43*2^32+1
> 25*2^64+1
> 21*2^128+1
> 207*2^256+1
> 223*2^512+1
> 1125*2^1024+1
> 2577*2^2048+1
> 3091*2^4096+1
> 9165*2^8192+1
>
>
> If there are no primes known and you are interested in searching
> these primes let me know so we can coordinate a team effort.
> My email is harsh@u...
>
> For the GFN's there is a team effort going on at