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A105170 Primes unnecessary for Goldbach's conjecture. 1
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; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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 unnecessary list to a million or so. So far, 3/5 of the primes are unnecessary.

LINKS

Table of n, a(n) for n=0..74.

Ed Pegg Jr, Material added 09 April 05.

EXAMPLE

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.

CROSSREFS

Sequence in context: A220293 A166307 A128464 * A162175 A178128 A330410

Adjacent sequences:  A105167 A105168 A105169 * A105171 A105172 A105173

KEYWORD

nonn

AUTHOR

Ed Pegg Jr, Apr 11 2005

STATUS

approved

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Last modified June 18 19:04 EDT 2021. Contains 345120 sequences. (Running on oeis4.)