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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

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  • $\begingroup$ I'm interested, these don't match anything on OEIS. $\endgroup$ – LeppyR64 Sep 8 '17 at 12:03
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    $\begingroup$ 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. $\endgroup$ – Gareth McCaughan Sep 8 '17 at 12:25
  • $\begingroup$ (The complement of the set is also not in OEIS.) $\endgroup$ – Gareth McCaughan Sep 8 '17 at 15:54
  • $\begingroup$ @GarethMcCaughan Yes, it is the latter, sorry if I made it ambiguous $\endgroup$ – Wen1now Sep 8 '17 at 23:42
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This has gone unsolved for too long. The answer is:

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

Note:

I have to admit, I just remembered a conversation in chat - important things that perked my memory included this message and this message.

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