"Is a number prime?" I've come up with a very efficient way of finding if a number is prime, using TI-BASIC for use with TI-83/84/+/SE calculators. I am trying to optimize it however possible.

:Input "NUMBER: ",A
:If A&lt;2 or fPart(A
:Then
:Disp "INVALID INPUT"
:Stop
:End
:0→B
:2→I
:While I&lt;A and not(B
:If 0=fPart(A/I
:1→B
:I+2→I
:If I=4
:3→I
:End
:If B
:Disp "NOT"
:Disp "PRIME"


A few notes:


Lines 2-6 are for validating input, and don't affect the effectiveness of the program.
The closing "s on line 4 and the last two lines are not necessary, but I added them so the syntax would highlight nicely here.
Lines 12-14 are for speeding up the loop doubly; instead of incrementing by 1 each time, it is by 2, with the If to offset the 4 to 3 on the first run.
The not(B was very efficient, to end the loop whenever a match to identify the number as a composite number is found.
I do not speak TI-BASIC, so I cannot review the style, coding conventions etc. But there are two possible optimizations:


If a number A is composite then it must have a factor that is less than or
equal to sqrt(A). So you can replace

:While I&lt;A and not(B


with (and I am just guessing the syntax):

:sqrt(A) -&gt; S
:While I&lt;=S and not(B


This  reduces the number of trial divisions substantially  if the input is a prime number.
Check the divisibility by 2 first, and then loop just over the odd numbers
I = 3, 5, 7, .... This saves you from checking

:If I=4
:3-&gt;I


in each loop iteration.