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Search: id:A128464
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| A128464 |
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Numbers of the form 30k+r, 0 < r < 30, that are possible lower bounds of twin prime pairs. |
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2
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| 11, 17, 29, 41, 47, 59, 71, 77, 89, 101, 107, 119, 131, 137, 149, 161, 167, 179, 191, 197, 209, 221, 227, 239, 251, 257, 269, 281, 287, 299, 311, 317, 329, 341, 347, 359, 371, 377, 389, 401, 407, 419, 431, 437, 449, 461, 467, 479, 491, 497, 509, 521, 527, 539
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For a 30k+r "wheel", r = 11,17,29 are the only possible values that can form a a lower twin prime pair. The 30k+r wheel gives the recurrence 1, 7,11,13,17,19,23,29 31,37,41,43,47,49,53,59 .. which is frequently used in prime number sieves to skip multiples of 2,3,5. The fact that adding 2 to 30k+1,7,13,19,23 will gives us a multiple of 3 or 5, precludes these numbers from being a lower member of a twin prime pair. This leaves us with r = 11,17,29 as the only possible cases to form a lower bound of a twin prime pair.
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EXAMPLE
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41 = 30*1 + 11, the lower part of the twin prime pair 41,43.
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PROGRAM
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(PARI) g(n) = forstep(x=11, n, 30, print1(x", "x+6", "x+18", "))
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CROSSREFS
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Sequence in context: A105886 A051634 A038918 this_sequence A105170 A111255 A060213
Adjacent sequences: A128461 A128462 A128463 this_sequence A128465 A128466 A128467
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), May 05 2007
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