Problems & Puzzles: Puzzles

Puzzle 382. KL(29207), Prime or Composite?

One more Prime Curio published is this one:

All numbers smaller than 35 + 57 + 1113 + 1719 + 2931 + ... + 2920729209 (note the Twin primes) in this form are composite and this is the first such number not yet proved to be composite or prime. It has 130433 digits and contains no prime factor less than 45267907. [Kulsha & Liaskovsky]

Let's call these numbers to be KL(P) = Σ [p^(p+2)], where p & p+2 are prime twins; p = 3, 5, 11, 17, 29, ..., P.

Question: Can you find a factor to KL(29207)?
 

Solutions came from Farideh Firoozbakht, Adam Stinchcombe, Mark Rodenkirch, Bernardo Boncompagni & Frederick Schneider.

All of them found that "151603073 is the smallest prime factor of  KL(29207)"

Mark added: "The others without factors for p< 50000 are: 30467,31247,31727,32441,34469,34511,34841,34961,36527,38459,44381. All others factors are available upon request"

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