Pierpont Prime

Author

Eric W. Weisstein
April 19, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PrimeNumbers/PierpontPrime.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PierpontPrime.html.

©2010 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

Take[Select[Union[Flatten[Outer[2^#1 3^#2+1&,Range[0,18],Range[0,12]]]],PrimeQ],50]//Timing

Powers of (10^(2^n))

Length[pp=Select[With[{exp=2^7},Union[Flatten[Table[2^m 3^n+1,{m,0,Floor[Log[2,10^exp]]},{n,0,Floor[Log[3,10^exp/2^m]]}]]]],PrimeQ]]//Timing

Length[pp=Select[With[{exp=2^8},Union[Flatten[Table[2^m 3^n+1,{m,0,Floor[Log[2,10^exp]]},{n,0,Floor[Log[3,10^exp/2^m]]}]]]],PrimeQ]]//Timing

Table[Count[pp,_?(#<10^(2^n)&)],{n,0,8}]

Length[pp=Select[With[{exp=2^10},Union[Flatten[Table[2^m 3^n+1,{m,0,Floor[Log[2,10^exp]]},{n,0,Floor[Log[3,10^exp/2^m]]}]]]],PrimeQ]]//Timing

Table[Count[pp,_?(#<10^(2^n)&)],{n,0,10}]

Largest Known

746190 digits (2^2478785 3 + 1)

IntegerLength[2^2478785 3+1]

PrimeQ[2^2478785 3+1]//Timing

1529928 digits (3*2^5082306+1)

IntegerLength[p=3*2^5082306+1]

PrimeQ[p]//Timing