e50.ps

%Implementation of "Smartest Sieve" from Sieve Timing :)
%Assumes symbol /primes is defined
/isPrime {
    /x exch def
    /ip true def
    /i 0 def
    /for2 {
        /p primes i get def
        x p mod 0 eq {
            /ip false def
        } {
            p p mul x le {
                /i i 1 add def
                for2
            } if
        } ifelse
    } def
    for2   
    ip     
} def

/primeSieve {
    /N exch def
    /primes N array def
    primes 0 2 put
    primes 1 3 put
    primes 2 5 put
    /primeLength 3 def
    /n 7 def
    /for1 {
        n isPrime {
            primes primeLength n put
            /primeLength primeLength 1 add def
        } if
        /n 2 n mul 3 mod 2 mul n add def
        n N lt {
            for1
        } if
    } def
    for1
} def

%Assumes symbol /primes is defined
/partialSum {
    /sum 0 def
    /high exch def
    /low exch def
    /k low def
    /for3 {
        /sum sum primes k get add def
        /k k 1 add def
        k high lt {
            for3
        } if
    } def
    for3
    sum
} def

/BOUND 1000000 def
%Method defines symbols /primes and /primeLength
%We do not use any return value
BOUND primeSieve
/ans 0 def
/maxChainLength 1 def
/lindex 0 def
/for4 {
    lindex primeLength lt {
        /hindex lindex maxChainLength add def
    hindex primeLength lt {
        /psum lindex hindex partialSum def
        /for5 {
            hindex primeLength lt psum BOUND lt and {
                psum isPrime {
                    /ans psum ans max def
                    /maxChainLength hindex lindex sub def
                } if
                /psum psum primes hindex get add def
                /hindex hindex 1 add def
                for5
            } if
        } def
        for5
        /lindex lindex 1 add def
        for4
    } if
    } if
} def
for4

ans pstack pop