# Primes of a certain form

[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

• I'm interested, these don't match anything on OEIS. Sep 8, 2017 at 12:03
• Just to be clear, do you mean (1) there is a property X parameterized by an integer n, and the n'th line shows the smallest prime with property X_n, or (2) there is a property X and the n'th line shows the n'th smallest prime with property X? I guess the latter but some of what you say suggests the former. Sep 8, 2017 at 12:25
• (The complement of the set is also not in OEIS.) Sep 8, 2017 at 15:54
• @GarethMcCaughan Yes, it is the latter, sorry if I made it ambiguous Sep 8, 2017 at 23:42

Primes that cannot be represented in the form $$\frac{pq+1}{p+q}$$ for primes $p,q$.