(12C+) how many primes between two numbers

[Don Shepherd]

Here is a cute little program for the 12c+ that will tell you the number of prime numbers between two numbers you specify. It takes a rather brute force approach, which is why I recommend it for the 12c+ and not the slower 12c.

It also uses the N financial register as a flag. If you set N=0, it will just tell you the number of primes between the two numbers you specify. If you set N to anything else, it will pause and show you (briefly) each prime that it finds, and give you the total primes at the end. I think this is a neat and easy way to use N as a flag.

To use the program, set N to 0 or non-zero depending upon whether you want to see each prime, then enter your range in X and Y (lower point in Y, upper point in X), then press R/S and be amazed. It works best if your range is under 1000 or 2000, because although the 12c+ is fast, it is still brute force.

Code:


01 sto 2
02 x<->y
03 sto 1
04 0
05 sto 3
06 rcl 1
07 2
08 /
09 frac
10 x=0
11 goto 13
12 goto 15
13 1
14 sto+1
15 3
16 sto 0
17 rcl 1
18 sqrt
19 sto 6
20 rcl 1
21 rcl 0
22 /
23 frac
24 x=0
25 goto 39
26 2
27 sto+0
28 rcl 6
29 rcl 0
30 x<=y
31 goto 20
32 rcl n
33 x=0
34 goto 37
35 rcl 1
36 pse
37 1
38 sto+3
39 2
40 sto+1
41 rcl 2
42 rcl 1
43 x<=y
44 goto 15
45 rcl 3

[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