## 1057 digit prime arithmetic progression of primes

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• Hi All 452558752*2459#+n*359463429*2459#+1 (n=0-7) describes an AP8 of 1056-1057 digit primes. sieved n=0-2,000,000,000 538,430,975 prp tests 11,482,783 prps
Message 1 of 2 , Apr 20, 2009
Hi All

452558752*2459#+n*359463429*2459#+1 (n=0-7) describes an AP8 of 1056-1057 digit primes.

sieved n=0-2,000,000,000
538,430,975 prp tests
11,482,783 prps
189,178,618,167 ap3s
543,008,443 ap4s (psuedo eg. 1,2,3,5 as only processed AP3's with an even difference)
3,117,826 ap5s
14,311 ap6s
64 ap7s
0 ap8s
extended 9 ap7s (0 ap8s)
extended 2459 ap6s (13 ap7s, 0 ap8s)
extended 624,016 ap5s (3548 ap6s, 10 ap7s, 1 ap8s)

cheers
Ken

Primality testing 452558752*2459#+0*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2473
Calling Brillhart-Lehmer-Selfridge with factored part 33.52%
452558752*2459#+0*359463429*2459#+1 is prime! (0.2870s+0.0019s)
Primality testing 452558752*2459#+1*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 33.37%

1/0
452558752*2459#+1*359463429*2459#+1 is prime! (0.2729s+0.0016s)
Primality testing 452558752*2459#+2*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 33.39%
452558752*2459#+2*359463429*2459#+1 is prime! (0.2729s+0.0016s)
Primality testing 452558752*2459#+3*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 33.45%
452558752*2459#+3*359463429*2459#+1 is prime! (0.2716s+0.0017s)
Primality testing 452558752*2459#+4*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2473
Running N-1 test using base 2503
Calling Brillhart-Lehmer-Selfridge with factored part 33.56%
452558752*2459#+4*359463429*2459#+1 is prime! (0.3667s+0.0017s)
Primality testing 452558752*2459#+5*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Calling Brillhart-Lehmer-Selfridge with factored part 33.38%
452558752*2459#+5*359463429*2459#+1 is prime! (0.2691s+0.0016s)
Primality testing 452558752*2459#+6*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 33.52%
452558752*2459#+6*359463429*2459#+1 is prime! (0.2702s+0.0017s)
Primality testing 452558752*2459#+7*359463429*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Calling Brillhart-Lehmer-Selfridge with factored part 33.44%
452558752*2459#+7*359463429*2459#+1 is prime! (0.2690s+0.0016s)
• ... Congratulations! http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. Ken now has the AP4 to AP8 records. The former AP8 record from 2003
Message 2 of 2 , Apr 21, 2009
Ken Davis wrote:
> 452558752*2459#+n*359463429*2459#+1 (n=0-7) describes an AP8 of 1056-1057
> digit primes.

Congratulations!
http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated.
Ken now has the AP4 to AP8 records.
The former AP8 record from 2003 was the oldest record for largest known AP.
The oldest is now an AP15 from 2005 when the page was created.

--
Jens Kruse Andersen
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