1+2*7^k is always divisible by 3 On Sat, Oct 24, 2015 at 11:55 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Dumb questions re primes.
Primes of the form 1+2^k are quite rare. ;-)
Primes of the form 1+2*3^k seem to be less rare.
Primes of the form 1+2*5^k seem to get rarer.
Primes of the form 1+2*7^k seem to be quite rare. (I don't have a fast machine, but I'm having trouble finding even one.)
Primes of the form 1+2*11^k seem to be less rare.
Also, how rare are primes of the form 1+2*p_1*p_2*p_3..., where p_i are odd primes (i.e., primes to the 1st power only) ?
(Perhaps these primes should be called "Euclid primes" after Euclid's proof of the infinite # of primes -- if they have no other name?)
Anything known about these distributions?
Also, is the discrete log particularly cheap to compute for any of these prime forms?
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