OFFSET
1,1
COMMENTS
Although there are 78498 primes < 10^6, only 3030 primes are required to form all even numbers < 10^6. There are 10581, 36308 and 123139 of these primes less than 10^7, 10^8 and 10^9, respectively. The asymptotic density of these primes appears to be 0. The number of these primes < x is roughly 0.85 sqrt(x log(x)).
Assuming the strong form of Goldbach's conjecture, Granville proves that thin sets of primes exist such that every even number >2 is the sum of two members of the set. - T. D. Noe, Apr 26 2006
LINKS
T. D. Noe, Table of n, a(n) for primes up to 10^6
T. D. Noe, Terms up to 10^9 (1.3 MB)
MATHEMATICA
ps={2, 3}; Do[pn=Select[2n-ps, PrimeQ]; If[Intersection[ps, pn]=={}, AppendTo[ps, Max[pn]]], {n, 4, 1000}]; Sort[ps]
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
T. D. Noe, Apr 26 2006
STATUS
approved