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5 , 53 , 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103

For example, 53 is the sixteenth prime. The fifteenth and seventeenth primes, 47 and 59, add up to 106, which is twice 53, thus 53 is a balanced prime.

When 1 was considered a prime number, 2 would have correspondingly been considered a balanced prime since 2 = (1 + 3)/2.


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When a prime is greater than the arithmetic mean of its two neighboring primes, it's called a Strong Prime . When it's less, it's called a Weak Prime .