(12C+) how many primes between two numbers

[Gamo]

Very nice program tested and work great !!

I just happen to see the example program to
"Generate Prime Number" from the HP-35S User Manual and I use that algorithm to
work on the HP-12C+ or Emulators.

I make some modification, instead of testing against square root I use X^2
this will run faster for large number.

Procedure:

If the input number is already prime the same number is display if not the next
prime larger than the previous number display.

FIX 0

n [R/S] display Prime Number [R/S] next Prime Number

Program:

Code:


01 STO 0  // Store integer value
02  3
03 STO 1  // Store 3 to start the test divisor
04 RCL 0
05  2
06  ÷
07 FRAC
08 X=0  // Tests for even number input
09 GTO 25  // This integer is an even number go ahead and branches to line 25 
10 RCL 0
11 RCL 1
12  ÷
13 FRAC 
14 X=0  // Test for a remainder of zero (not prime)
15 GTO 27  // Not prime tries next possibility 
16 RCL 1
17 ENTER
18  x
19 RCL 0
20 X≤Y  // Test to see whether all possible factors have been tried
21 GTO 30  // If all have been tried, branches to line 30 to display prime number
22  2
23 STO+1  // Increment the divisor  
24 GTO 10
25  1  // Increment integer if input an even number
26 GTO 28
27  2  // Increment integer to search for a prime number
28 STO+0
29 GTO 02
30 RCL 0  // Finally got the precious prime number
31 R/S  // Stop and add one to previous prime number
32  1
33  +
34  GTO 01  // Start over to generate the next prime number

Remark: Is there a better algorithm than this to search faster?

Gamo