Math Is Fun Forum

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

To find out if x is prime using only addition!

Let x= ANY ODD "+" INTEGER >3

Let y=(x/3) Rounded down

IF any of the below are TRUE then x is composite OTHERWISE x is prime.

x+1=EVEN triangular number
x+1+2= ODD triangular number
x+1+2+3=EVEN triangular number
x+1+2+3+4= ODD triangular number
x+1+2+3+4+5=EVEN triangular number
x+1+2+3+4+5+6= ODD triangular number
........etc.
Until x+1+2+3......+y

EXAMPLE

x=35
x/3=11+2/3 rounded down =11
Therefore y=11
x+1=35+1=36 36 is an EVEN triangular number
Therefore 35 is composite

EXAMPLE

x=17
x/3=5+2/3 rounded down =5
Therefore y=5
x+1=17+1=18
x+1+2=18+2=20
x+1+2+3=20+3=23
x+1+2+3+4=23+4=27
x+1+2+3+4+5=27+5=32
Therefore 17 is prime

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