-- Project Euler #10: Summation of Primes

-- Sum of all primes below 2,000,000.

-- Answer: 142913828922

--

-- Odd-only Sieve of Eratosthenes: arr[k] represents 2k+1. Size 1,000,000

-- covers odd numbers up to 1,999,999. Mark composites during `mutate`

-- (set only, no reads), then `lend` and sum via O(1) `nth` reads.

list 1000000 (1 push) repeat box 'sv let

sv (

0 0 set must -- 1 is not prime

1

(dup 2 mul 1 plus dup mul 2000000 lt) -- (2i+1)^2 < 2M

(

'i let

i 2 mul 1 plus 'p let -- p = 2i+1

i i 1 plus mul 2 mul -- initial j = 2*i*(i+1)

(dup 1000000 lt)

(dup (0 set must) dip p plus) while

drop

i 1 plus

) while

drop

) mutate 'svb let

svb (

'data let

2 1 -- sum=2 (even prime), k=1

(dup 1000000 lt)

(

'k let

'data k nth must 1 eq (k 2 mul 1 plus plus) () if

k 1 plus

) while

drop

) lend

swap free print