[seqfan] Re: Sieving method for composite numbers described / used in A146071

Maximilian Hasler maximilian.hasler at gmail.com
Fri Oct 31 20:49:55 CET 2008

I think the following primes will never appear:


I obtained them (certainly not in a n optimized way) using the idea
from my previous mail:

| next; t=bitor(1<<primepi(k),t));bittest(t,primepi(p)) |



(which is not exactly equal to A145834 but extends that function
defined on composites to the domain of all numbers.)



On Fri, Oct 31, 2008 at 15:14, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
> I think you have A145834(n) > n/2 - 2 or something alike,
> so any prime that does not appear in due time in this sequence will
> never appear in it and thus will not appear in A146071.
> I don't know either if a method *using* the complete prime
> factorization of the numbers can be considered as a "sieving" method
> for prime numbers.
> It's a bit like "if n>1 is not prime, subtract 1 and start over, else
> stop" (which of course yields all primes).
> Maximilian
> On Fri, Oct 31, 2008 at 13:00, Alexander Povolotsky <apovolot at gmail.com> wrote:
>> Hi,
>> Would the sieving method for composite numbers, with which I came up in
>> A146071,
>> produce ALL prime  numbers (so far I don't see 13 there ... ;-) ) ?
>> If NOT - then could one define / predict what prime numbers will be not
>> generated by below described sieving method for composite numbers ?
>> Was this sieving method described / used before ?
>> Thanks,
>> Best Regards,
>> Alexander R. Povolotsky
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