## C(x,6)+1

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• p = C(342397*2^36022+4,6)+1 is a binomial prime with 65093 digits. It was found and proved with PrimeForm/GW. Earlier David found a top-5000 prime C(x,4)+1
Message 1 of 2 , Nov 17 3:30 PM
p = C(342397*2^36022+4,6)+1 is a binomial prime with 65093 digits.
It was found and proved with PrimeForm/GW.
Earlier David found a top-5000 prime C(x,4)+1 with a different method:
http://groups.yahoo.com/group/primeform/message/6036
The next logical challenge would be C(x,8)+1 which looks harder.

If 2 out of 6 consecutive numbers are completely factored
then a prp on form C(x,6)+1 just becomes BLS provable.
My lucky search went through the Prime Pages database with p of top-5000 size.
Thanks to Chris for maintaining the database. It has been very helpful before.
342397*2^36022+1 was found by Vincent S. Wighman with Proth.exe in 1998.
That helper enabled the 33.34% proof:

D:>pfgw -t -hhelper.txt c6.txt
PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing (342397*2^36022+4)*(342397*2^36022+3)*(342397*2^36022+2)*
(342397*2^36022+1)*(342397*2^36022)*(342397*2^36022-1)/6!+1
[N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.txt
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 33.34%
(342397*2^36022+4)*(342397*2^36022+3)*(342397*2^36022+2)*(342397*2^36022+1)*
(342397*2^36022)*(342397*2^36022-1)/6!+1 is prime! (2620.8548s+0.0162s)

PrimeForm cannot parse C(x,y) for x>2^31 so a longer expression was used.

--
Jens Kruse Andersen
• Jens, ... Excellent! I do like your ideas for reprocessing the list. David
Message 2 of 2 , Nov 17 4:22 PM
Jens,

> My lucky search went through the Prime Pages database with
> p of top-5000 size.

Excellent! I do like your ideas for reprocessing the list.

David
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