After slight help from chatGPT, it took me some time to get this working, and using VirtualAlloc rather than a static buffer

sieve_win64.asm

format PE64 CONSOLE
entry main

include 'C:\util\fasmw17330\INCLUDE\WIN64a.INC'
include 'C:\util\fasmw17330\INCLUDE\API\KERNEL32.INC'

;section '.data' data readable writeable
    ; primes dq 2
    ;sieve db 1000000 dup 1
    define sieve r13
;    sieve_end equ $
    sieve_len equ 10000 ;  $-sieve
section '.text' code readable executable
;    global main
;    extern printf


main:
    ; set up stack frame
    push rbp
    mov rbp, rsp
    mov r8,sieve_len+64
    xor rax,rax
    invoke  VirtualAlloc,0,r8,MEM_COMMIT+MEM_RESERVE,PAGE_READWRITE
    test rax,rax
    jnz alloc_good

    lea rcx,[error_alloc]
    call [printf]
    jmp end_program

alloc_good:
    mov r13,rax
    ; initialize the array
    mov rdi,r13
    mov rax, 0101010101010101h  ; 1=prime
    mov rcx,sieve_len / 8
    cld
    rep stosq ; mark everything prime

    ; sieve algorithm
    mov rcx, 3 ; start at 3

sieve_loop:
    cmp rcx, sieve_len
    jge print_primes

    cmp byte[sieve + rcx],0
    je sieve_skip   ; already cleared (not prime)

    mov rbx, rcx
    add rbx, rcx
sieve_mark:
    cmp rbx, sieve_len
    jge sieve_skip

    mov byte [sieve + rbx], 0 ; not prime
    add rbx, rcx
    jmp sieve_mark
sieve_skip:
    add rcx, 2
    jmp sieve_loop

    ; print out primes
print_primes:
    lea rcx,[primes_msg]
    call [printf]
    mov r12, 1
print_loop:
    cmp byte [sieve + r12], 0
    je print_skip

    push rax ; align stack before call
    lea rcx, [prime_format]
    mov rdx, r12
    ;mov rdi, qword [primes + rcx*8 - 8]
    xor rax, rax
    call [printf]
    add rsp, 8 ; restore stack pointer after call

print_skip:
    add r12,2
    cmp r12, sieve_len
    jl  print_loop

    invoke  VirtualFree,r13,0,MEM_RELEASE
    ; clean up stack frame
end_program:
    mov rsp, rbp
    pop rbp
    invoke  ExitProcess,0

section '.rdata' data readable
    prime_format db "%ld ", 0
    error_alloc  db 'error in virtual alloc',0
    primes_msg db 'primes:',0

section '.idata' import data readable
    library msvcrt, 'msvcrt.dll',\
            kernel32, 'kernel32.dll'

    import msvcrt, \
        printf, 'printf',\
        getchar, 'getchar',\
        putchar, 'putchar',\
        setmode, '_setmode'