More on twin primes and Pythagorean triples

Pat B. wrote a response to my last post on the number 867-5309. In that post I pointed out that: 8675309 is a prime. 8675309 is a twin prime (8675311 is also prime). 8675309 is the hypotenuse of a (primitive) Pythagorean triple: 86753092 = 24602602+83191412. Pat asked: What is the smallest number that would meet…