## Re: [PrimeNumbers] 11593 digit sexy prime pair

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• ... Congrats. As far as I know, that is the largest proven pair, and the largest prp pairs are in http://mersenneforum.org/showthread.php?t=11381#10 I don t
Message 1 of 3 , May 6, 2009
Ken Davis wrote:
> Not sure who (if anyone, as the Chris's prime pages doesn't track them) is
> interested in this type of prime but fyi
>
> ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5
> ((3369281*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+11
>
> are 11593 digit sexy prime pair.

Congrats. As far as I know, that is the largest proven pair, and the largest
I don't think anybody is maintaining a record page.
I only posted the former 11004-digit proven record to

--
Jens Kruse Andersen
• Hi All, A gigantic cousin pair (to go with the sexy pair) ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1
Message 2 of 3 , May 8, 2009
Hi All,

A gigantic cousin pair (to go with the sexy pair)

((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1
((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5

with 11594 digitS

Primality testing ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 33.32%
Proof incomplete rerun with -x41241
((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 is PRP! (19.4720s+0.0029s)

rerunning as instructed yields

Primality testing ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 33.32%
1/41240
8193/41240
16385/41240
24577/41240
32769/41240
40961/41240
((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+1 is prime! (30.4132s+0.0024s)

Primality testing ((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 9007
Running N+1 test using discriminant 9013, base 1+sqrt(9013)
Running N+1 test using discriminant 9013, base 2+sqrt(9013)
Calling N+1 BLS with factored part 33.34% and helper 0.01% (100.02% proof)
((8907956*35+16)*587502*9001#*(587502*9001#+1)+210)*(587502*9001#-1)/35+5 is prime! (279.4887s+0.0025s)

Cheers
Ken
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