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balanced prime
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(Definition)
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If for the given  th prime  the equality
is true, then  is said to be a balanced prime. That is, the arithmetic mean of the given prime, the prime immediately below and the one immediately above, is equal to the middle prime. The first few are 5, 53, 157, 173, 211, 257, 263, 373, listed in A006562 of Sloane's OEIS. As of 2006, the largest known balanced prime is
 , discovered by David Broadhurst and François Morain using FastECPP and PrimeForm.
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"balanced prime" is owned by PrimeFan.
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(view preamble)
Cross-references: PrimeForm, OEIS, arithmetic mean, equality, prime
This is version 1 of balanced prime, born on 2007-01-23.
Object id is 8811, canonical name is BalancedPrime.
Accessed 496 times total.
Classification:
| AMS MSC: | 11A41 (Number theory :: Elementary number theory :: Primes) |
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Pending Errata and Addenda
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