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I have been playing around with a program I wrote implementing the sieve of Eratosthenes, and I stumbled across some prime numbers that, when you average them with all the primes less than or equal to them, you get an integer. I was wondering if these are of any interest in modern research, or in any part of mathematics? Does anyone know anything about such primes?

Here are the first eight:

83

241

6599

126551

1544479

4864121

60686737

991184221

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    $\begingroup$ See the relevant OEIS entry. $\endgroup$
    – user296602
    Aug 22, 2018 at 2:53

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