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+--- Thread: (12C+) how many primes between two numbers (/thread-13215.html)
(12C+) how many primes between two numbers - Don Shepherd - 06-30-2019 11:30 PM
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 3RE: (12C+) how many primes between two numbers - Gamo - 08-22-2019 06:48 AM
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 numberRemark: Is there a better algorithm than this to search faster?
Gamo