A balanced prime is a prime number that 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,
The first few balanced primes are
5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103 (sequence A006562 in OEIS).
For example, 53 is the sixteenth prime. The fifteenth and seventeenth primes, 47 and 59, add up to 106, half of which is 53, thus 53 is a balanced prime.
When 1 was considered a prime number, 2 would have correspondingly been considered the first balanced prime since
It is conjectured that there are infinitely many balanced primes.
Three consecutive primes in arithmetic progression is sometimes called a CPAP-3. A balanced prime is by definition the second prime in a CPAP-3. As of 2009 the largest known CPAP-3 with proven primes has 7535 digits found by David Broadhurst and François Morain:
The value of n is not known.
Famous quotes containing the words balanced and/or prime:
“Much of the ill-tempered railing against women that has characterized the popular writing of the last two years is a half-hearted attempt to find a way back to a more balanced relationship between our biological selves and the world we have built. So women are scolded both for being mothers and for not being mothers, for wanting to eat their cake and have it too, and for not wanting to eat their cake and have it too.”
—Margaret Mead (1901–1978)
“Few white citizens are acquainted with blacks other than those projected by the media and the so—called educational system, which is nothing more than a system of rewards and punishments based upon one’s ability to pledge loyalty oaths to Anglo culture. The media and the “educational system” are the prime sources of racism in the United States.”
—Ishmael Reed (b. 1938)