The name   cuban   has nothing to do with   Cuba  (the country),   but has to do with the
fact that cubes   (3rd powers)   play a role in its definition.



Some definitions of cuban primes

   primes which are the difference of two consecutive cubes.
   primes of the form:   (n+1)3 - n3.
   primes of the form:   n3 - (n-1)3.
   primes   p   such that   n2(p+n)   is a cube for some   n>0.
   primes   p   such that   4p = 1 + 3n2.


Cuban primes were named in 1923 by Allan Joseph Champneys Cunningham.



Task requirements

   show the first   200   cuban primes   (in a multi─line horizontal format).
   show the   100,000th   cuban prime.
   show all cuban primes with commas   (if appropriate).
   show all output here.


Note that   cuban prime   isn't capitalized   (as it doesn't refer to the nation of Cuba).



Also see

   Wikipedia entry:     cuban prime.
   MathWorld entry:   cuban prime.
   The OEIS entry:     A002407.     The   100,000th   cuban prime can be verified in the   2nd   example   on this OEIS web page.


function isprime( n as ulongint ) as boolean
    if n mod 2 = 0 then return false
    for i as uinteger = 3 to int(sqr(n))+1 step 2
        if n mod i = 0 then return false
    next i
    return true
end function
 
function diff_cubes( n as uinteger ) as ulongint
    return 3*n*(n+1) + 1
end function
 
function padto( n as uinteger, s as integer ) as string
    dim as string outstr=""
    dim as integer k = len(str(n))
    for i as integer = 1 to s-k
        outstr = " " + outstr
    next i
    return outstr + str(n)
end function
 
dim as integer nc = 0, i = 1, di
while nc < 100000
    di = diff_cubes(i)
    if isprime(di) then
        nc += 1
        if nc <= 200 then 
            print padto(di,8);" ";
            if nc mod 10 = 0 then print
        end if
        if nc = 100000 then
            print : print : print di
            exit while
        end if
    end if
    i += 1
wend