(30b) Some number theory progs

[Gerald H]

Finds smallest factor of odd integer input. Returns input & factor or 0 if prime.
0 P0
1 Lbl 02
2 STO 0
3 √
4 Math
5 Up
6 Up
7 Input
8 STO 2
9 3
10 STO 1
11 Lbl 00
12 RCL 0
13 RCL 1
14 /
15 Math
16 Up
17 Input
18 GT 01
19 RCL 0
20 RCL 1
21 RTN
22 Lbl 01
23 2
24 STO+ 1
25 RCL 1
26 RCL 2
27 ?≤
28 GT 00
29 RCL 0
30 0
31 =
32 RTN


Finds next prime after input integer
0 P1
1 Lbl 04
2 STO 0
3 2
4 /
5 Math
6 Up
7 Input
8 GT 03
9 1
10 STO- 0
11 Lbl 03
12 2
13 STO+ 0
14 RCL 0
15 Call02
16 GT 03
17 RCL 0
18 RTN

Returns an input-digit random integer, max digits 12
0 P2
1 Lbl 05
2 Input
3 1
4 2
5 Input
6 ?<
7 GF 06
8 R↓
9 Lbl 06
10 1
11 0
12 Swap
13 Y^X
14 Rand
15 *
16 Math
17 Up
18 Up
19 Input
20 RTN

Returns an input-digit random prime
0 P3
1 Lbl 07
2 Call05
3 Call04
4 RTN

Returns a 2*input-digit semi-prime
0 P4
1 STO 3
2 Call07
3 STO 4
4 RCL 3
5 Call07
6 RCL 4
7 *
8 RTN

Returns approx number of primes less than input
0 P5
1 Input
2 Input
3 Input
4 Ln
5 1
6 -
7 /
8 Math
9 Up
10 Up
11 Input
12 RTN

I'm sure these progs are not optimized, I haven't really got the hang of programming on the 30b & would be pleased for optimization suggestions.