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