Copyright 5/1/2010 Justin Coslor
Midpoint Parity of Prime Number Neighborhoods (The Odd Or Even 
Parity of Midpoints Between Consecutive Prime Numbers).
 
3 (4) 5 [4 is an even midpoint] 5-3=2 2-1=1 between Twin Primes
5 (6) 7 [6 is an even midpoint] 7-4=2 2-1=1 between Twin Primes
7 (9) 11 [9 is an odd midpoint] 11-7=4 4-1=3 between
11 (12) 13 [12 is an even midpoint] 13-11=2 2-1=1 between Twin Primes
13 (15) 17 [15 is an odd midpoint] 17-13=4 4-1=3 between
17 (18) 19 [18 is an even midpoint] 19-17=2 2-1=1 between Twin Primes
19 (21) 23 [21 is an odd midpoint] 23-19=4 4-1=3 between
23 (26) 29 [26 is an even midpoint] 29-23=6 6-1=5 between
29 (30) 31 [30 is an even midpoint] 31-29=2 2-1=1 between Twin Primes
31 (34) 37 [34 is an even midpoint] 37-31=6 6-1=5 between
37 (39) 41 [39 is an odd midpoint] 41-37=4 4-1=3 between
41 (42) 43 [42 is an even midpoint] 43-41=2 2-1=1 between Twin Primes
43 (45) 47 [45 is an odd midpoint] 47-43=4 4-1=3 between
47 (49) 51 [49 is an odd midpoint] 51-47=4 4-1=3 between
etc. So you can see that sometimes the midpoints between consecutive prime 
numbers is even and sometimes the midpoint between consecutive prime 
numbers is odd. When there is one number between consecutive primes then 
the midpoint is even, and when there are three between consecutive primes 
then the midpoint is odd, and when there are five between consecutive 
prime numbers then the midpoint is even. So it continues in that 
alternativing manner of the midpoints being even, odd, even, etc 
depending on how many numbers are between two consecutive primes..