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Thursday, 28 November 2013

Prime pyramid-adjacent primes-2

This is with reference to my earlier blog-same title
I had shown row 8 as follows-1,6,7,4,3,2,5,8 where each pair of adjacent numbers add upto a prime viz 1+6=7,6+7=13,7+4=11,4+3=7,3+2=5,2+5=7,5+8=13
The further rows can be formed as follows-
a)As 8+9=17 (a prime) ,we can simply add 9 to get 1,6,7,4,3,2,5,8,9
b)As 9+10=19(a prime),we can simply add 10 to get 1,6,7,4,3,2,5,8 ,9,10
c)As 10+11=21 which is not a prime we have to modify numbers in row (b)
For this we follow the same position upto 3,add the nos from 2 to 10 in the reverse way and then add 11
We will get 1,6,7,4,3,(10,9,8,5,2),11
d)12 can be added as 11+12=23,giving us 1,6,7,4,3,10,9,8,5,2,11,12
e)13 cannot be added as 12+13=25 is not a prime.The change is made as follows-
1,6,7,(12,11,2,5,8,9,10,3,4),13
Further rows are filled up in the same fashion-
f) 1,6,7,12,11,2,5,8,9,10,(13,4,3),14
h)1,6,7,12,11,2,5,8,9,10,13,4,3,14,15
j)1,6,7,12,11,2,5,8,9,10,13,4,3,14,15,16
k)1,6,7,12,11,2,5,8,9,10,13,4,3,(16,15,14),17
l)1,6,7,12,11,2,(17,14,15,16,3,4,13,10,9,8,5),18
m)1,6,7,12,11,2,17,14,15,16,3,4,13,10,9,8,5,18,19
n) 1,6,7,12,11,2,17,14,15,16,3,4,13,10,(19,18,5,8,9),20
We can follow the same procedure for further rows.  

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