Thanks! p=1 (mod 3) also kills off 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, etc. p^2=1 (mod 3) [p=2=-1 (mod 3)] kills off even powers of the other primes /= 3. Hans Havermann suggests: http://oeis.org/A005234 'Primorial primes' (I'd never heard of this term before) are interesting, but I'm also allowing any subsequence of the primes, so long as they contain 2. At 11:09 AM 10/24/2015, James Buddenhagen wrote:
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?