Problem 128 is a really interesting problem about prime numbers. It reads

**A hexagonal tile with number 1 is surrounded by a ring of six hexagonal tiles, starting at “12 o’clock” and numbering the tiles 2 to 7 in an anti-clockwise direction.**

**New rings are added in the same fashion, with the next rings being numbered 8 to 19, 20 to 37, 38 to 61, and so on. The diagram below shows the first three rings.**

**By finding the difference between tile ***n* and each its six neighbours we shall define PD(*n*) to be the number of those differences which are prime.

**For example, working clockwise around tile 8 the differences are 12, 29, 11, 6, 1, and 13. So PD(8) = 3.**

**In the same way, the differences around tile 17 are 1, 17, 16, 1, 11, and 10, hence PD(17) = 2.**

**It can be shown that the maximum value of PD(***n*) is 3.

**If all of the tiles for which PD(***n*) = 3 are listed in ascending order to form a sequence, the 10th tile would be 271.

**Find the 2000th tile in this sequence.**

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