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[True story] I was looking through some old files and I found a file called 'lowest prime not of a certain form' (of course, it was for some maths question which I don't recall anymore). It looked at the integers in order 1,2,3,... and outputted the first primes that satisfied some property. These were the first few lines of the output:

73 107 131 157 173 179 193 227 263 277 283 313 317 331 367 383 389

Looking at the code, I eventually worked out what this program did. But, with just the output, can you work out what type of primes it outputs?

tl;dr These primes are the smallest primes that satisfy some property X, find X