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Search: id:A105170
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| A105170 |
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Primes unnecessary for Goldbach's conjecture. |
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+0
2
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| 11, 17, 29, 41, 59, 67, 71, 73, 89, 97, 103, 127, 137, 149, 151, 163, 173, 179, 181, 191, 193, 197, 223, 227, 229, 233, 239, 241, 257, 263, 271, 277, 311, 317, 331, 347, 349, 353, 359, 367, 373, 379, 389, 397, 409, 419, 433, 443, 461, 463, 467, 479, 487, 499, 503, 541, 547, 557, 563, 571, 577, 587, 593, 599, 607, 613, 617, 619, 631, 641, 647, 653, 659, 661, 677
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Jacques Tramu confirmed and extended these results. If all of the unnecessary primes are excluded, all even numbers up to 60000 can be obtained. Not proved, a proof of Goldbach's conjecture would be easier. It would be good to verify the unecessary list to a million or so. So far, 3/5th of the primes are unnecessary.
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LINKS
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Ed Pegg Jr, Material added 09 April 05.
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EXAMPLE
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3 and 5 are necessary for 3+5=8. 7 is necessary for 5+7 = 12. 11 seems to be a completely unnecessary prime, so I marked it as such. 13 is then needed for 5+13 = 18 (can't use 7+11=18, since I've ruled 11 unnecessary.) And so on, looking at each prime in turn, and determining whether they are necessary or unnecessary.
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CROSSREFS
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Adjacent sequences: A105167 A105168 A105169 this_sequence A105171 A105172 A105173
Sequence in context: A051634 A038918 A128464 this_sequence A111255 A060213 A073651
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KEYWORD
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nonn
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AUTHOR
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Ed Pegg Jr (ed(AT)mathpuzzle.com), Apr 11 2005
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