Unsolved problems in number theory | Classes of prime numbers

Balanced prime

In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number , where n is its index in the ordered set of prime numbers, For example, 53 is the sixteenth prime; the fifteenth and seventeenth primes, 47 and 59, add up to 106, and half of that is 53; thus 53 is a balanced prime. (Wikipedia).

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Interprime | Prime number | Strong prime | Prime gap | Primes in arithmetic progression | Number theory | Arithmetic mean