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 [number theory] sieving with a_i mod p_i jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 09/11/2014, 08:00 PM (This post was last modified: 09/11/2014, 08:02 PM by jaydfox.) (09/11/2014, 08:24 AM)tommy1729 Wrote: {0 mod 2, 0 mod 3 , 0 mod 5 , ... 0 mod prime 't' } does not define a certain a mod b. Rather it sieves out possibilities of a mod b. Its like 0 mod 2 , 0 mod 3 , 0 mod 5 gives : 1,7,11,13,17,19,23,29 mod 30. A similar thing happens with a_i mod p_i. But maybe that is what you actually meant (to say). regards tommy1729 Hmm, maybe we're talking about different things. I'm talking about an a_i that gives the respective remainders mod p_i, all at the same time, not individually. I agree that for sieving, we care about a single match, so we get back a set of sieved (or unsieved) numbers. The only numbers that are 0 mod 2, 0 mod 3, 0 mod 5 (all at the same time, not individually) are the numbers that are 0 mod 30. The only numbers that are 1 mod 2, 2 mod 3, 1 mod 5 are the numbers that are 11 mod 30. So by giving me a set of a_i's to go with the p_i's, like a_i={1, 2, 1} and p_i={2, 3, 5}, I can give you back a new "a" to go with product(p_i): a=11 and primorial(5)=30. In this sense, giving me a set of a_i's in the range 0 <= a_i < p_i is just equivalent to giving me a fixed a in the range 0 <= a < primorial(max(p_i)) In light of this, then yes, having unfixed a_i's is an interesting problem in its own right, as long as we can agree that it's just another way of looking at a fixed value of a. Edit: So for example, sieving numbers against 1 mod 2, 2 mod 3, and 1 mod 5, is like sieving them against 11 mod 2, 11 mod 3, and 11 mod 5. Hopefully that made sense...End Edit And I reserve the right to be wrong. ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread [number theory] sieving with a_i mod p_i - by tommy1729 - 09/09/2014, 01:10 AM RE: [number theory] sieving with a_i mod p_i - by jaydfox - 09/10/2014, 04:50 PM RE: [number theory] sieving with a_i mod p_i - by tommy1729 - 09/10/2014, 08:27 PM RE: [number theory] sieving with a_i mod p_i - by jaydfox - 09/11/2014, 01:47 AM RE: [number theory] sieving with a_i mod p_i - by tommy1729 - 09/11/2014, 08:24 AM RE: [number theory] sieving with a_i mod p_i - by jaydfox - 09/11/2014, 08:00 PM RE: [number theory] sieving with a_i mod p_i - by tommy1729 - 09/12/2014, 07:28 AM RE: [number theory] sieving with a_i mod p_i - by tommy1729 - 09/11/2014, 11:40 AM

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