Terms greater than 1000 are often only strong pseudoprimes.
Factors of these numbers are of the form p = 2*n*k + 1, just like the repunit numbers, but the PRP tests are significantly slower since there is not a fast mod() property like the repunits, where (number mod Rn) can be calculated with a folding of the digits at length n in base b. However, numbers of this form b^p - (b-1)^p seem to be prime with greater relative frequency than the repunits. While the repunits have a linear fit coefficient that approaches 0.56145948 (see link below for a Generalized Repunit Conjecture), this sequence currently has a linear fit coefficient of 0.22559. -
Paul Bourdelais, Jul 06 2023
