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%I #36 Jan 23 2019 19:25:24
%S 5,11,13,17,19,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,
%T 103,107,109,113,127,131,137,139,149,167
%N 2-provable primes: Primes p expressible as x+y, where the prime factors of x and y are precisely the primes less than sqrt(p).
%C There cannot be any terms > 169 because the least possible value for x+y once 13 is included in the set of prime factors is 347 > 17^2. For p > 347, the list of factors required in x or y also includes 17, pushing the minimal p to 1429 (714 + 715). This in turn adds the next 5 primes to the list, pushing the minimal value of x+y exponentially upward relative to p.
%e The primes less than sqrt(167) are 2, 3, 5, 7, and 11, and 167 = 2*3*3*5 + 7*11, so 167 is in this sequence.
%K nonn,fini,full
%O 1,1
%A _Charlie Neder_, Jan 21 2019