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How to deal with that type of question ? Are there infinite prime numbers beginning by 2? I know that there infinite prime ending by 1,3,7 and 9 by Dirichlet’s prime number theorem.

I’am only interested by the first term in special case 2. Not for a generalization. I think that this specific case provide a simpler proof than the generalization.

DINEDINE
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  • I guess so, and I think you can prove this by estimates on prime gaps/densities. – Trebor Apr 05 '19 at 14:19
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    The distribution of first digits tends to uniformity: https://arxiv.org/abs/0811.3302 – Jam Apr 05 '19 at 14:20
  • @Jam thanks you – DINEDINE Apr 05 '19 at 14:23
  • I disagree with your decision to close this one as a duplicate. This problem is MUCH simpler and does not need a complex solution of a more complex problem. The starting sequence in this case is a single digit. – Oldboy Apr 05 '19 at 15:00

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