' Puzzlet #019.
' Find a sequence of six 5-digit prime numbers
' a,b,c,d,e,  such that b = a + 2, c = b + 4,
' ... f = e + 10.   This is a span of 30 integers,
' of which only six are allowed to be prime.
' Example: 21557,21559,21563,21569,21577,21587.
' There are four other sequences to find.
' By Dave Ellis.

declare Prime(p: int )
declare PokeNewPrime(p: int)
declare InSequence()
declare PrintSequence()
def n: int
def primeArray[7]: int
openconsole
print "Searching primes ..." : print

print "   a     b     c     d     e     f"
print
print "       = a+2 = b+4 = c+6 = d+8 =e+10"
print

for n = 10001 to 99997 #2
    if Prime(n)
        PokeNewPrime(n)
        if InSequence()
            PrintSequence()
        endif
    endif
next n

print: print "No more found."
print: print "Press any key to exit ..."
do: until inkey$ <> ""
closeconsole
end

sub Prime(p)
' If p is a prime number,
' returns 1, else returns 0.
def flag, i, root: int
if p = 2 | p = 3
    flag = -1
else
    if p % 2 = 0
        flag = 0
    else
        root = int (sqrt(p))
        i = 3
        do
            flag = -1       
            if p % i = 0
                flag = 0
            endif
            i = i + 2
        until ((flag = 0) | (i > root)))
    endif
endif
return flag
   
sub pokeNewPrime(p)
' Shuffles primeArray contents from position
' 6 to position 2 downwards by one position,
' overwriting as it goes. Position 1 content
' is permanently lost.  New prime p is poked
' into primArray[6].   
def i, j: int
for i = 1 to 5
    j = i + 1
    primeArray[i] = primeArray[j]
next i
primeArray[6] = p
return    

sub inSequence()
' If primeArray contents are in sequence as
' defined in the introductory REMs, returns
' 1, otherwise returns 0.
def flag, i: int
flag = -1
i = 1
do
    if primeArray[i + 1] <> i*2 + primeArray[i]
        flag = 0
    endif
    i = i + 1
until flag = 0 | i = 6
return flag

sub printSequence()   
' Prints out the contents of primeArray.   
def i: int
for i = 1 to 6
    print using ("######", primeArray[i]),
next i
print
return