Pandigital never prime

Consider the number 100020
If you change one of its digits, you never get a prime number:

100020= $2^2\times 3\times 5\times 1667$
200020= $2^2\times 5\times 73\times 137$
300020= $2^2\times 5\times 7\times 2143$
400020= $2^2\times 3\times 5\times 59\times 113$
500020= $2^2\times 5\times 23\times 1087$
600020= $2^2\times 5\times 19\times 1579$
700020= $2^2\times 3^2\times 5\times 3889$
800020= $2^2\times 5\times 13\times 17\times 181$
900020= $2^2\times 5\times 11\times 4091$

100020= $2^2\times 3\times 5\times 1667$
110020= $2^2\times 5\times 5501$
120020= $2^2\times 5\times 17\times 353$
130020= $2^2\times 3\times 5\times 11\times 197$
140020= $2^2\times 5\times 7001$
150020= $2^2\times 5\times 13\times 577$
160020= $2^2\times 3^2\times 5\times 7\times 127$
170020= $2^2\times 5\times 8501$
180020= $2^2\times 5\times 9001$
190020= $2^2\times 3\times 5\times 3167$

100020= $2^2\times 3\times 5\times 1667$
101020= $2^2\times 5\times 5051$
102020= $2^2\times 5\times 5101$
103020= $2^2\times 3\times 5\times 17\times 101$
104020= $2^2\times 5\times 7\times 743$
105020= $2^2\times 5\times 59\times 89$
106020= $2^2\times 3^2\times 5\times 19\times 31$
107020= $2^2\times 5\times 5351$
108020= $2^2\times 5\times 11\times 491$
109020= $2^2\times 3\times 5\times 23\times 79$

100020= $2^2\times 3\times 5\times 1667$
100120= $2^3\times 5\times 2503$
100220= $2^2\times 5\times 5011$
100320= $2^5\times 3\times 5\times 11\times 19$
100420= $2^2\times 5\times 5021$
100520= $2^3\times 5\times 7\times 359$
100620= $2^2\times 3^2\times 5\times 13\times 43$
100720= $2^4\times 5\times 1259$
100820= $2^2\times 5\times {71}^2$
100920= $2^3\times 3\times 5\times {29}^2$

100000= $2^5\times 5^5$
100010= $2\times 5\times 73\times 137$
100020= $2^2\times 3\times 5\times 1667$
100030= $2\times 5\times 7\times 1429$
100040= $2^3\times 5\times 41\times 61$
100050= $2\times 3\times 5^2\times 23\times 29$
100060= $2^2\times 5\times 5003$
100070= $2\times 5\times 10007$
100080= $2^4\times 3^2\times 5\times 139$
100090= $2\times 5\times 10009$

100020= $2^2\times 3\times 5\times 1667$
100021= $29\times 3449$
100022= $2\times 13\times 3847$
100023= $3\times 7\times 11\times 433$
100024= $2^3\times 12503$
100025= $5^2\times 4001$
100026= $2\times 3^2\times 5557$
100027= $23\times 4349$
100028= $2^2\times 17\times 1471$
100029= $3\times 33343$


What is the smallest pandigital number (in base 10) with that property? (*)
(*) All the numbers you get when changing one digit must be pandigital too.


[My timing: < 1 sec]