Problems & Puzzles: Puzzles

Puzzle 362. A sequence of primes.   Andrew Rupinski submit the following puzzle: Consider the sequence of primes: 3 5 17 257 65537 4294967311 1229782942255939601 88962710886098567818446141338419231 255302062200114858892457591448999891874349780170241684791167583265041 ... This extremely sparse subset of primes has a remarkable property. Question. Thus I ask you what this property is, and consequently what the next 3 primes in the sequence are?

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