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:

NB. replace concatenates at various ranks and in boxes to avoid fill
NB. the curtailed prefixes (}:\) with all of 0..9 (i.10) with the beheaded suffixes (}.\.)
NB. under the antibase 10 representation (10&#.inv)
replace=: ([: ; <@}:\ ,"1 L:_1 ([: < (i.10) ,"0 1 }.)\.)&.(10&#.inv)

NB. primable tests if one of the replacements is prime
primable=: (1 e. 1 p: replace)&>

unprimable=: -.@:primable

assert 0 1 -: unprimable 193 200