interprime


Given two consecutive odd primes, the ith prime pi and the next one, pi+1, an interprimeMathworldPlanetmath n is the arithmetic meanMathworldPlanetmath of the two:

n=pi+pi+12

Thus, n-pi=pi+1-n, so alternatively

n=pi+pi+1-pi2=pi+1-pi+1-pi2.

For example, given the 269th and 270th primes, 1723 and 1733, the interprime is 1728, and indeed 1728-1723=1733-1728=5. Interprimes themselves are of course always composite, though not always even. An interprime between a twin primeMathworldPlanetmath will always be even, while an interprime between the second (ending in 3 in base 10) and third (ending in 7 in base 10) member of a prime quadrupletMathworldPlanetmath will always be odd and be divisible by 5.

The first few interprimes are 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, etc., listed in A024675 of Sloaneā€™s OEIS.

Title interprime
Canonical name Interprime
Date of creation 2013-03-22 18:08:25
Last modified on 2013-03-22 18:08:25
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A51
Related topic MinimalAndMaximalNumber