Problems & Puzzles: Puzzles

Puzzle 550.- Consecutive primes producing semiprimes

JM Bergot sent the following nice puzzle.

5*7  + 11*13 = 178 = 2*89 (√)
7*11 + 13*17 = 298 = 2*149 (√)
11*13 + 17*19 = 466 = 2*233 (√)
13*17 + 19*23 = 658 = 2*7*47 (X)

 Q. Find a longer run of consecutive primes adding this way to semiprimes?

Contributions came from Jan van Delden, Antoine Verroken, Emmanuel Vantieghem

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Jan, Antoine & Emmanuel wrote:

The first occurrence of a sequence of 4 semiprimes starts with prime 17017471.