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Search: id:A118371
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| A118371 |
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Fastest growing sequence of primes satisfying Goldbach's conjecture. |
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1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 (noe(AT)sspectra.com), Apr 26 2006
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LINKS
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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)
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MATHEMATICA
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ps={2, 3}; Do[pn=Select[2n-ps, PrimeQ]; If[Intersection[ps, pn]=={}, AppendTo[ps, Max[pn]]], {n, 4, 1000}]; Sort[ps]
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CROSSREFS
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Cf. A105170 (primes unnecessary for Goldbach's conjecture).
Sequence in context: A101044 A077321 A082885 this_sequence A038917 A134266 A062252
Adjacent sequences: A118368 A118369 A118370 this_sequence A118372 A118373 A118374
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KEYWORD
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nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Apr 26 2006
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