

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
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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



