Noticed for all primes $< 5000000$ there are $174190$ primes of form $6n+1$ and $174321$ of $6n-1$.
At no point did the number of $6n+1$ primes overtake $6n-1$.
Any reason for primes having a bias towards $6n-1$?
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1It might be related to this specific prime number race, although it's not the same. – Thomas Preu Aug 18 '22 at 22:34
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1The $2006$ Monthly article Prime Number Races (by Granville & Martin) cited in quid's answer in the linked dupe is a good place to begin studies on this topic. – Bill Dubuque Aug 18 '22 at 22:49
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See also Wikipedia's article on Chebyshev's_bias – Bill Dubuque Aug 18 '22 at 22:55
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Chebychev's bias (the nonresidues seem to be preferred). On the long run, the ratio tends to $1$ and I guess the lead switches infinite many often like in the race between $4n+1$ and $4n+3$ , but I am not sure. – Peter Aug 18 '22 at 22:56