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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, 01:47 AM (09/10/2014, 08:27 PM)tommy1729 Wrote: Thank you for your reply and intrest Jay ! However Im not sure what you computed. (...) But then you write a_i .. 28..33 (...) Does that mean that for any of 28,29,... 33 as a fixed value of a_i we get the same result ? Many interpretations are possible I think. Im betting you are considering a fixed a_i and 0..27 1204 means that for any fixed a_i between 0 and 27 we get the same value : 1204. Is my guess correct ? Exactly what I meant! For a fixed a_i of 0 (or 1, or 2, or 27, etc.), I found 1204 "primes" in the range of 101 to 10000 inclusive. Quote:Note that in my OP - which appears confusing apparantly - the a_i are not neccessarily fixed. So we could consider 1 mod 2 ,1 mod 3, 2 mod 5, 6 mod 7, 5 mod 11 etc I assume fixed a_i are easier to study perhaps. Well, my modular arithmetic is rusty, but it seems to me that {1 mod 2, 1 mod 3, 2 mod 5, 6 mod 7, 5 mod 11}, as a set, defines a unique number mod 2*3*5*7*11. Assuming my educated guess is right, you basically are fixing a_i, though not limited to the same range as initially defined. So I think it still makes sense to speak in terms of a fixed a_i, if perhaps we relax the restriction on the size of a_i (up to primorial(p_i)-1 or something like that). ~ 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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