Problems & Puzzles: Puzzles

Puzzle 485. Farideh's guess Farideh Firoozbakht posed this puzzle:  I found the following four nice equations.               2*5 - 3 = 7                ( first four primes )            3*7 - 2*5 = 11              ( first five primes )         5*11 - 2*3*7 = 13             ( first six primes )      2*7*13 - 3*5*11 = 17          ( first seven primes ) Note that the largest prime is at the right hand of the equation. I guess that if n>7,  for the first n primes, there is no such equation. Q1. Can you probe the Farideh's "guess"? Q2. Can you probe the Farideh's "guess" if the largest prime can be in any side of the equation?

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Contribution came from Jacques Tramu (who decided not to be there "just watching the wheels go round and round").

Note: Perhaps you will agree with me than more than a solution the Tramu's contribution open a new problem. So until we get new solutions to Q1, Q2 & now to Q3, is impossible not to say - reminding that delicious title/article from F. Smarandache- that at the moment we have "Only Problems, Not Solutions"... L

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Jacques wrote:

I found no answer for n> 7, so I added

Q3 : use first n primes and allow any number of primes in the right side of the equation,
and found :

n= 8 2*13*17 - 5*7*11 = 3*19
n= 9 2*5*11*13 - 3*19*23 = 7*17
n= 10 2*3*17*29 - 5*13*23 = 7*11*19
n= 11 5*7*23*29 - 3*13*19*31 = 2*11*17
n= 13 17*23*31*41 - 2*3*7*11*29*37 = 5*13*19

and no more...

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