Optimize TI-BASIC Prime Numbers Finder

Question

I wrote a program to find all the prime numbers up to N on my TI-84, however, it is quite slow for any number above, like, 50. Are there any ways to optimize my code?

(I added comments using //)

Input N
{2}→L2
For(I,3,N,2) // Loop through every odd number up to N starting at 3
1→J
0→H
√(I)→S
While L2(J)≤S and H=0 // checks every previously found prime # less than sqrt(I)
If remainder(I,L2(J))=0
1→H // used to break the loop
J+1→J
End
If H=0 // if no numbers divided evenly, add it to the list
augment(L2, {I})→L2 
End
Disp L2 

Thanks!

Answer 1

For factorization, the state of the art (as of like 1999, but also today as far as I know) is something like Rob Gaebler's ABIGSIV: https://www.ticalc.org/archives/files/fileinfo/79/7923.html

The essential idea is to use the "wheel" method. Make a list of all the prime numbers between 1 and 2*3*5*7 and stash that list in L1; then, do trial-division by L1+210*I all at once. The important thing is to maximize the amount of time you spend doing divisions and minimize the amount of time you spend doing bookkeeping.

• Martin R: You suggest a faster algorithm. Perhaps you can clarify how this is a review of the posted code.