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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 

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