Problem Statement

As used here, all unprimeable numbers   (positive integers)   are always expressed in base ten.

───── Definition from OEIS ─────: Unprimeable numbers are composite numbers that always remain composite when a single decimal digit of the number is changed.

───── Definition from Wiktionary   (referenced from Adam Spencer's book) ─────: (arithmetic)   that cannot be turned into a prime number by changing just one of its digits to any other digit.   (sic)

Unprimeable numbers are also spelled:   unprimable. All one─ and two─digit numbers can be turned into primes by changing a single decimal digit.

190   isn't unprimeable,   because by changing the zero digit into a three yields   193,   which is a prime.

The number   200   is unprimeable,   since none of the numbers   201, 202, 203, ··· 209   are prime, and all the other numbers obtained by changing a single digit to produce   100, 300, 400, ··· 900,   or   210, 220, 230, ··· 290   which are all even.

It is valid to change   189   into   089   by changing the   1   (one)   into a   0   (zero),   which then the leading zero can be removed,   and then treated as if the   "new"   number is   89.

Show all output here, on this page.

Let's start with the solution:

unprimeable?: function [n][
    if prime? n -> return false
    nd: to :string n
    loop.with:'i nd 'prevDigit [
        loop `0`..`9` 'newDigit [
            if newDigit <> prevDigit [
                nd\[i]: newDigit
                if prime? to :integer nd -> return false
            ]
        ]
        nd\[i]: prevDigit
    ]
    return true
]

cnt: 0
x: 1
unprimeables: []
while [cnt < 600][
    if unprimeable? x [
        unprimeables: unprimeables ++ x
        cnt: cnt + 1
    ]
    x: x + 1
]

print "First 35 unprimeable numbers:"
print first.n: 35 unprimeables
print ""
print ["600th unprimeable number:" last unprimeables]