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 A118371 Fastest growing sequence of primes satisfying Goldbach's conjecture. 3
 2, 3, 5, 7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 79, 83, 101, 107, 109, 113, 131, 139, 157, 167, 199, 211, 251, 269, 281, 283, 293, 307, 313, 337, 383, 401, 421, 431, 439, 449, 457, 491, 509, 521, 523, 569, 601, 643, 673, 691, 701, 769, 773, 811, 839, 863, 881 (list; graph; refs; listen; history; text; internal format)
 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 Andrew Granville, Refinements of Goldbach's conjecture and the Generalized Riemann Hypothesis 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 Cf. A105170 (primes unnecessary for Goldbach's conjecture). Sequence in context: A154579 A233134 A082885 * A330968 A153591 A038917 Adjacent sequences: A118368 A118369 A118370 * A118372 A118373 A118374 KEYWORD nice,nonn AUTHOR T. D. Noe, Apr 26 2006 STATUS approved

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Last modified June 24 01:53 EDT 2024. Contains 373661 sequences. (Running on oeis4.)