"Primorial" primes. Hmmmm.. OK, here's a new(?) sequence for OEIS, perhaps called a "Goedel sequence" G(n): n in N maps to 2^d0*3^d1*5^d2*7^d3*11^d4*... d0 is 0'th bit of n; d1 is the 1st bit of n; d2 is the 2nd bit of n; d3 is the 3rd bit of n; etc. G(0) = 1 G(1) = 2 G(2) = 3 G(3) = 2*3 = 6 G(4) = 5 G(5) = 2*5 = 10 G(6) = 3*5 = 15 G(7) = 2*3*5 = 30 G(8) = 7 G(9) = 2*7 = 14 G(11) = 2*3*7 = 42 G(13) = 2*5*7 = 70 G(15) = 2*3*5*7 = 210 G(17) = 2*11 = 22 G(19) = 2*3*11 = 66 G(21) = 2*5*11 = 110 etc. A Goedelian prime would be an odd number n such that G(n)+1 is prime. G(1)+1 = 2+1 = 3 is prime G(3)+1 = 6+1 = 7 is prime G(5)+1 = 10+1 = 11 is prime G(7)+1 = 2*3*5+1 = 31 is prime G(9)+1 = 2*7+1 = 15 is NOT prime G(11)+1 = 2*3*7+1 = 43 is prime G(13)+1 = 2*5*7+1 = 71 is prime G(15)+1 = 2*3*5*7+1 = 211 is prime G(17)+1 = 2*11+1 = 23 is prime G(19)+1 = 2*3*11+1 = 67 is prime G(21)+1 = 2*5*11+1 = 111 is NOT prime etc. At 11:20 AM 10/24/2015, Hans Havermann wrote:
On Oct 24, 2015, at 12:55 PM, Henry Baker <hbaker1@pipeline.com> wrote:
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) ?