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 March 9th, 2016, 09:11 AM #1 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 Subsets and product of primes Hi, Let P be the set of consecutive prime numbers from 2 to p {2,3,5,7,11,.....,p} We split the set in 2 subsets P1 and P2 such as P1 U P2 = P and intersection of P1 and P2 = Empty set. Example P = {2,3,5,7,11,13,17,19} P1={2,5,7,11,13} P2={3,17,19} Or P1={3,7,17,19} P2={2,5,11,13} Let us compute A=product of all elements of the set P1 B=product of all elements of the set P2 Example A=2*5*7*11*13=10010 B=3*17*19=969 We want the minimal value of M=A+B P={2,3} M=5 P={2,3,5} M=11 P={2,3,5,7} M=29 P={2,3,5,7,11} M=97 P={2,3,5,7,11,13} M=353 and so on I have not found the sequence in OEIS Is there any way to have an approximation of M in relation with Card(P) 2----> 5 3----> 11 4....? 29 5----> 97 6----> 353 Card(P)---> M = f(Card*P)? Thank you for any clue or idea March 10th, 2016, 05:28 AM #2 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 Sorry I did a mistake while computing Card(p)=6 It is 347 instead of 353. Someone corrected me. Hence the sequence is on OEIS https://oeis.org/A182987 Tags primes, product, subsets Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post neelmodi Number Theory 1 August 11th, 2014 06:50 AM kankan Number Theory 9 March 23rd, 2014 12:52 PM proglote Number Theory 21 July 8th, 2011 09:59 AM Agno Number Theory 1 May 9th, 2011 03:49 PM self_study Number Theory 8 March 14th, 2010 04:04 AM

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