(pp-1)/2 is prime: {27, 2187,...}

[Dean Hickerson]

Robert G. Wilson v" <rgwv at kspaint.com> wrote:

> All that I found < 10^7 are 27, 2187 and 159323.

That last one should be 1594323.

The point of my message was that you don't have to check all perfect powers,
only those of the form 3^p with p prime.  The first 12 perfect powers  pp
such that  (pp-1)/2  is prime are:

    3^3 = 27,
    3^7 = 2187,
    3^13 = 1594323,
    3^71 = 7509466514979724803946715958257547,
    3^103,   3^541,   3^1091,   3^1367,   3^1627,   3^4177,   3^9011,   3^9551

Dean Hickerson
dean at math.ucdavis.edu