Hyperbolic prime triples

There are (probably infinitely) many triples of prime numbers P1 < P2 < P3 such as Pi+Pj*Pk is a square number for all combinations (i,j,k) with i!=j!=k.

Here is an example: 4049,126001,130051

Find the triple with the largest P3 < 180,000

Answer format: comma separated list

Example: 4049,126001,130051

[My timing: 95 sec]