Initial Query

Here is the description of a new assembly language: * 8 registers (R1, R2, R3, R4, R5, R6, R7, R8) that can hold integers. * 1 flag that can hold a boolean value (True or False). * 100 memory addresses (0-99) that can hold integers. * 1 instruction pointer that points to the current instruction being executed. Each instruction is of the form OP ARG1 ARG2 ... where ARGn can be either a register (e.g., R1) or a constant (e.g., 10). Labels are written with a lowercase word followed by colon. The assembly language supports the following instructions: * SET Rx C: Assigns the value C to register Rx. * ADD Rx Ry Rz: Adds the values of Ry and Rz and stores the result in Rx. * (similarly for SUB, MUL, DIV, MOD) * EQ Rx Ry: Sets the flag to True if Rx and Ry are equal, False otherwise. * (similarly for NEQ, LT (Rx < Ry), LTE, GT, GTE) * INC/DEC Rx: Increments/Decrements the value of Rx by one. * JMP L: Jumps to label L unconditionally. * JT/JF (jump if true / jump if false) L: Jumps to label L if the is set or not set. * LOAD Rx M: Loads the value at memory address M into register Rx. * STORE Rx M: Stores the value of register Rx into memory address M. * HCF: Stops the program (with pizzazz) Given this assembly language, write a program that puts the first 20 prime numbers in memory cells 0..19

LLM Generation

Query

Here is the description of a new assembly language: * 8 registers (R1, R2, R3, R4, R5, R6, R7, R8) that can hold integers. * 1 flag that can hold a boolean value (True or False). * 100 memory addresses (0-99) that can hold integers. * 1 instruction pointer that points to the current instruction being executed. Each instruction is of the form OP ARG1 ARG2 ... where ARGn can be either a register (e.g., R1) or a constant (e.g., 10). Labels are written with a lowercase word followed by colon. The assembly language supports the following instructions: * SET Rx C: Assigns the value C to register Rx. * ADD Rx Ry Rz: Adds the values of Ry and Rz and stores the result in Rx. * (similarly for SUB, MUL, DIV, MOD) * EQ Rx Ry: Sets the flag to True if Rx and Ry are equal, False otherwise. * (similarly for NEQ, LT (Rx < Ry), LTE, GT, GTE) * INC/DEC Rx: Increments/Decrements the value of Rx by one. * JMP L: Jumps to label L unconditionally. * JT/JF (jump if true / jump if false) L: Jumps to label L if the is set or not set. * LOAD Rx M: Loads the value at memory address M into register Rx. * STORE Rx M: Stores the value of register Rx into memory address M. * HCF: Stops the program (with pizzazz) Given this assembly language, write a program that puts the first 20 prime numbers in memory cells 0..19

Output

Here's the assembly program that generates the first 20 prime numbers and stores them in memory addresses 0 to 19: 

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    SET R1 0          ; Prime count
    SET R3 0          ; Memory index
    SET R2 2          ; First candidate (2)

main_loop:
    SET R4 20
    GTE R1 R4         ; Check if 20 primes found
    JT end_program

    ; Prime check for R2
    SET R7 1          ; Assume prime
    SET R4 2
    EQ R4 R2          ; Is candidate 2?
    JT prime_yes
    SET R4 2
    MOD R4 R2 R4      ; Check evenness
    EQ R4 0
    JT prime_no
    SET R4 3          ; Divisor start

loop_divisors:
    MUL R5 R4 R4
    GT R5 R2          ; Divisor^2 > candidate?
    JT prime_yes
    MOD R5 R2 R4      ; Check divisibility
    EQ R5 0
    JT prime_no_in_loop
    ADD R4 R4 2       ; Next divisor
    JMP loop_divisors

prime_no_in_loop:
    SET R7 0
    JMP after_prime_check

prime_no:
    SET R7 0

prime_yes:
    SET R7 1

after_prime_check:
    EQ R7 1
    JT store_prime
    JMP next_candidate

store_prime:
    STORE R2 R3       ; Store prime
    INC R3
    INC R1

next_candidate:
    SET R4 2
    EQ R4 R2          ; Was current prime 2?
    JT increment_to_3
    ADD R2 R2 2       ; Next odd number
    JMP main_loop

increment_to_3:
    SET R2 3          ; After 2 comes 3
    JMP main_loop

end_program:
    HCF               ; Halt
**How it works:** 1. **Initialization:** Starts with candidate number 2 (the first prime) 2. **Prime Check:** - Special case for 2 (only even prime) - Checks odd numbers starting from 3 - Efficiently tests divisors up to √n (using divisor² > n) 3. **Storage:** Stores primes sequentially in memory as they're found 4. **Optimization:** After 2, only checks odd numbers (increments by 2) 5. **Termination:** Stops after finding and storing 20 primes The program uses registers for: - R1: Prime count - R2: Current candidate number - R3: Memory index - R4-R7: Temporary calculations and flags The HCF instruction gracefully stops the program once all 20 primes are stored.

Extract Code

I extracted the following code from that output: 

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SET R1 0          ; Prime count
    SET R3 0          ; Memory index
    SET R2 2          ; First candidate (2)

main_loop:
    SET R4 20
    GTE R1 R4         ; Check if 20 primes found
    JT end_program

    ; Prime check for R2
    SET R7 1          ; Assume prime
    SET R4 2
    EQ R4 R2          ; Is candidate 2?
    JT prime_yes
    SET R4 2
    MOD R4 R2 R4      ; Check evenness
    EQ R4 0
    JT prime_no
    SET R4 3          ; Divisor start

loop_divisors:
    MUL R5 R4 R4
    GT R5 R2          ; Divisor^2 > candidate?
    JT prime_yes
    MOD R5 R2 R4      ; Check divisibility
    EQ R5 0
    JT prime_no_in_loop
    ADD R4 R4 2       ; Next divisor
    JMP loop_divisors

prime_no_in_loop:
    SET R7 0
    JMP after_prime_check

prime_no:
    SET R7 0

prime_yes:
    SET R7 1

after_prime_check:
    EQ R7 1
    JT store_prime
    JMP next_candidate

store_prime:
    STORE R2 R3       ; Store prime
    INC R3
    INC R1

next_candidate:
    SET R4 2
    EQ R4 R2          ; Was current prime 2?
    JT increment_to_3
    ADD R2 R2 2       ; Next odd number
    JMP main_loop

increment_to_3:
    SET R2 3          ; After 2 comes 3
    JMP main_loop

end_program:
    HCF               ; Halt

PyFunc

Resulting in output: False