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March 9th, 2016, 09:11 AM   #1
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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
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March 10th, 2016, 05:28 AM   #2
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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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